Antiparticle

Encyclopedia

Corresponding to most kinds of particles

, there is an associated

and opposite electric charge

. For example, the antiparticle of the electron

is the positively charged antielectron, or positron

, which is produced naturally in certain types of radioactive decay

.

The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an antiproton

and a positron can form an antihydrogen

atom, which has almost exactly the same properties as a hydrogen atom. This leads to the question of why the formation of matter after the Big Bang

resulted in a universe consisting almost entirely of matter, rather than being a half-and-half mixture of matter and antimatter

. The discovery of CP violation

helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate.

Particle-antiparticle pairs can annihilate

each other, producing photon

s; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography

.

Antiparticles are produced naturally in beta decay

, and in the interaction of cosmic ray

s in the Earth's atmosphere. Because charge is conserved, it is not possible to create an antiparticle without either destroying a particle of the same charge (as in beta decay) or creating a particle of the opposite charge. The latter is seen in many processes in which both a particle and its antiparticle are created simultaneously, as in particle accelerator

s. This is the inverse of the particle-antiparticle annihilation process.

Although particles and their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles. The neutron, for example, is made out of quarks, the antineutron

from antiquarks, and they are distinguishable from one another because neutrons and antineutrons annihilate each other upon contact. However, other neutral particles are their own antiparticles, such as photon

s, the hypothetical graviton

s, and some WIMPs. These can annihilate with themselves.

s by Paul Dirac

, Carl D. Anderson found that cosmic-ray collisions produced these particles in a cloud chamber

— a particle detector

in which moving electron

s (or positrons) leave behind trails as they move through the gas. The electric charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a magnetic field

. Positrons, because of the direction that their paths curled, were at first mistaken for electrons travelling in the opposite direction. Positron paths in a cloud-chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios.

The antiproton

and antineutron

were found by Emilio Segrè and Owen Chamberlain

in 1955 at the University of California, Berkeley

. Since then, the antiparticles of many other subatomic particles have been created in particle accelerator experiments. In recent years, complete atoms of antimatter

have been assembled out of antiprotons and positrons, collected in electromagnetic traps.

Solutions of the Dirac equation

contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amounts of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle

, no other electron could fall into them. Sometimes, however, one of these negative-energy particles could be lifted out of this Dirac sea

to become a positive-energy particle. But, when lifted out, it would leave behind a

s in his 1930 paper

s, and not proton

s.

Dirac was aware of the problem that his picture implied an infinite negative charge for the universe. Dirac tried to argue that we would perceive this as the normal state of zero charge. Another difficulty was the difference in masses of the electron and the proton. Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until Hermann Weyl

proved that hole theory was completely symmetric between negative and positive charges. Dirac also predicted a reaction + → + , where an electron and a proton annihilate to give two photons. Robert Oppenheimer

and Igor Tamm

proved that this would cause ordinary matter to disappear too fast. A year later, in 1931, Dirac modified his theory and postulated the positron, a new particle of the same mass as the electron. The discovery of this particle the next year removed the last two objections to his theory.

However, the problem of infinite charge of the universe remains. Also, as we now know, bosons also have antiparticles, but since bosons do not obey the Pauli exclusion principle (only fermions do), hole theory does not work for them. A unified interpretation of antiparticles is now available in quantum field theory

, which solves both these problems.

. This opens the way for virtual pair production or annihilation in which a one particle quantum state may

and renormalization

of a quantum field theory. It also opens the way for neutral particle mixing through processes such as the one pictured here, which is a complicated example of mass renormalization.

(

(

where

. Properties of antiparticles can be related to those of particles through this. If

where the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have

One may try to quantize an electron field

without mixing the annihilation and creation operators by writing

where we use the symbol

s, we have to have the operators satisfy canonical anti-commutation relations. However, if one now writes down the Hamiltonian

then one sees immediately that the expectation value of

So one has to introduce the charge conjugate

where

where the first sum is over positive energy states and the second over those of negative energy. The energy becomes

where

is defined as the state with no particle or antiparticle,

.

This approach is due to Vladimir Fock

, Wendell Furry and Robert Oppenheimer

. If one quantizes a real scalar field

, then one finds that there is only one kind of annihilation operator; therefore, real scalar fields describe neutral bosons. Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.

reached a pictorial understanding of the fact that the particle and antiparticle have equal mass

precisely in the form of diagrams. Richard Feynman

later gave an independent systematic derivation of these diagrams from a particle formalism, and they are now called Feynman diagram

s. Each line of a diagram represents a particle propagating either backward or forward in time. This technique is the most widespread method of computing amplitudes in quantum field theory today.

Since this picture was first developed by Ernst Stueckelberg

, and acquired its modern form in Feynman's work, it is called the

Particle physics

Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, there is an associated

**antiparticle**with the same massMass

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

and opposite electric charge

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

. For example, the antiparticle of the electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

is the positively charged antielectron, or positron

Positron

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

, which is produced naturally in certain types of radioactive decay

Radioactive decay

Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...

.

The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an antiproton

Antiproton

The antiproton is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy....

and a positron can form an antihydrogen

Antihydrogen

Antihydrogen is the antimatter counterpart of hydrogen. Whereas the common hydrogen atom is composed of an electron and proton, the antihydrogen atom is made up of a positron and antiproton...

atom, which has almost exactly the same properties as a hydrogen atom. This leads to the question of why the formation of matter after the Big Bang

Baryogenesis

In physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...

resulted in a universe consisting almost entirely of matter, rather than being a half-and-half mixture of matter and antimatter

Antimatter

In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

. The discovery of CP violation

CP violation

In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...

helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate.

Particle-antiparticle pairs can annihilate

Annihilation

Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....

each other, producing photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography

Positron emission tomography

Positron emission tomography is nuclear medicine imaging technique that produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide , which is introduced into the body on a...

.

Antiparticles are produced naturally in beta decay

Beta decay

In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

, and in the interaction of cosmic ray

Cosmic ray

Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...

s in the Earth's atmosphere. Because charge is conserved, it is not possible to create an antiparticle without either destroying a particle of the same charge (as in beta decay) or creating a particle of the opposite charge. The latter is seen in many processes in which both a particle and its antiparticle are created simultaneously, as in particle accelerator

Particle accelerator

A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s. This is the inverse of the particle-antiparticle annihilation process.

Although particles and their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles. The neutron, for example, is made out of quarks, the antineutron

Antineutron

The antineutron is the antiparticle of the neutron with symbol . It differs from the neutron only in that some of its properties have equal magnitude but opposite sign. It has the same mass as the neutron, and no net electric charge, but has opposite baryon number...

from antiquarks, and they are distinguishable from one another because neutrons and antineutrons annihilate each other upon contact. However, other neutral particles are their own antiparticles, such as photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s, the hypothetical graviton

Graviton

In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...

s, and some WIMPs. These can annihilate with themselves.

### Experiment

In 1932, soon after the prediction of positronPositron

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

s by Paul Dirac

Paul Dirac

Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

, Carl D. Anderson found that cosmic-ray collisions produced these particles in a cloud chamber

Cloud chamber

The cloud chamber, also known as the Wilson chamber, is a particle detector used for detecting ionizing radiation. In its most basic form, a cloud chamber is a sealed environment containing a supersaturated vapor of water or alcohol. When a charged particle interacts with the mixture, it ionizes it...

— a particle detector

Particle detector

In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify high-energy particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a...

in which moving electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s (or positrons) leave behind trails as they move through the gas. The electric charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

. Positrons, because of the direction that their paths curled, were at first mistaken for electrons travelling in the opposite direction. Positron paths in a cloud-chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios.

The antiproton

Antiproton

The antiproton is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy....

and antineutron

Antineutron

The antineutron is the antiparticle of the neutron with symbol . It differs from the neutron only in that some of its properties have equal magnitude but opposite sign. It has the same mass as the neutron, and no net electric charge, but has opposite baryon number...

were found by Emilio Segrè and Owen Chamberlain

Owen Chamberlain

Owen Chamberlain was an American physicist, and Nobel laureate in physics for his discovery, with collaborator Emilio Segrè, of antiprotons, a sub-atomic antiparticle.-Biography:...

in 1955 at the University of California, Berkeley

University of California, Berkeley

The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

. Since then, the antiparticles of many other subatomic particles have been created in particle accelerator experiments. In recent years, complete atoms of antimatter

Antimatter

In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

have been assembled out of antiprotons and positrons, collected in electromagnetic traps.

### Hole theory

... the development of quantum field theoryQuantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

made the interpretation of antiparticles as holes unnecessary, even though it lingers on in many textbooks.

— Steven WeinbergSteven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....

inThe quantum theory of fields, Volume 1: Foundations, p. 14, ISBN 0-521-55001-7

Solutions of the Dirac equation

Dirac equation

The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amounts of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle

Pauli exclusion principle

The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...

, no other electron could fall into them. Sometimes, however, one of these negative-energy particles could be lifted out of this Dirac sea

Dirac sea

The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons...

to become a positive-energy particle. But, when lifted out, it would leave behind a

*hole*

in the sea that would act exactly like a positive-energy electron with a reversed charge. These he interpreted as "negative-energy electrons" and attempted to identify them with protonElectron hole

An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s in his 1930 paper

*A Theory of Electrons and Protons*However, these "negative-energy electrons" turned out to be positronPositron

The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

s, and not proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s.

Dirac was aware of the problem that his picture implied an infinite negative charge for the universe. Dirac tried to argue that we would perceive this as the normal state of zero charge. Another difficulty was the difference in masses of the electron and the proton. Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until Hermann Weyl

Hermann Weyl

Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...

proved that hole theory was completely symmetric between negative and positive charges. Dirac also predicted a reaction + → + , where an electron and a proton annihilate to give two photons. Robert Oppenheimer

Robert Oppenheimer

Julius Robert Oppenheimer was an American theoretical physicist and professor of physics at the University of California, Berkeley. Along with Enrico Fermi, he is often called the "father of the atomic bomb" for his role in the Manhattan Project, the World War II project that developed the first...

and Igor Tamm

Igor Tamm

Igor Yevgenyevich Tamm was a Soviet physicist and Nobel laureate who received most prestigious Nobel Prize in Physics, jointly with Pavel Alekseyevich Cherenkov and Ilya Frank, for the discovery of Cherenkov radiation, made in 1934.-Biography:Tamm was born in Vladivostok, Russian Empire , in a...

proved that this would cause ordinary matter to disappear too fast. A year later, in 1931, Dirac modified his theory and postulated the positron, a new particle of the same mass as the electron. The discovery of this particle the next year removed the last two objections to his theory.

However, the problem of infinite charge of the universe remains. Also, as we now know, bosons also have antiparticles, but since bosons do not obey the Pauli exclusion principle (only fermions do), hole theory does not work for them. A unified interpretation of antiparticles is now available in quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, which solves both these problems.

## Particle-antiparticle annihilation

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles. Reactions such as + → + (the two-photon annihilation of an electron-positron pair) is an example. The single-photon annihilation of an electron-positron pair, + → , cannot occur in free space because it is impossible to conserve energy and momentum together in this process. However, in the Coulomb field of a nucleus the translational invariance is broken and single-photon annihilation may occur. The reverse reaction (in free space, without an atomic nucleus) is also impossible for this reason. In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principleUncertainty principle

In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

. This opens the way for virtual pair production or annihilation in which a one particle quantum state may

*fluctuate*into a two particle state and back. These processes are important in the vacuum stateVacuum state

In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...

and renormalization

Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

of a quantum field theory. It also opens the way for neutral particle mixing through processes such as the one pictured here, which is a complicated example of mass renormalization.

## Properties of antiparticles

Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugationC-symmetry

In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.-Charge reversal in electromagnetism:...

(

**C**), parity (**P**), and time reversalT-symmetry

T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

(

**T**) operators. If denotes the quantum state of a particle (**n**) with momentum**p**, spin**J**whose component in the z-direction is σ, then one haswhere

**n**denotes the charge conjugate state,^{c}*i.e.*, the antiparticle. This behaviour under**CPT**is the same as the statement that the particle and its antiparticle lie in the same irreducible representation of the Poincaré groupPoincaré group

In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.-Simple explanation:...

. Properties of antiparticles can be related to those of particles through this. If

**T**is a good symmetry of the dynamics, thenwhere the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have

- the same mass
**m** - the same spin state
**J** - opposite electric chargeElectric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

s**q**and**-q**.

## Quantum field theory

*This section draws upon the ideas, language and notation of canonical quantization*

of a quantum field theory

.Canonical quantization

In physics, canonical quantization is a procedure for quantizing a classical theory while attempting to preserve the formal structure of the classical theory, to the extent possible. Historically, this was Werner Heisenberg's route to obtaining quantum mechanics...

of a quantum field theory

Quantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

.

One may try to quantize an electron field

Field (physics)

In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

without mixing the annihilation and creation operators by writing

where we use the symbol

*k*to denote the quantum numbers*p*and σ of the previous section and the sign of the energy,*E(k)*, and*a*denotes the corresponding annihilation operators. Of course, since we are dealing with fermion_{k}Fermion

In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s, we have to have the operators satisfy canonical anti-commutation relations. However, if one now writes down the Hamiltonian

Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...

then one sees immediately that the expectation value of

*H*need not be positive. This is because*E(k)*can have any sign whatsoever, and the combination of creation and annihilation operators has expectation value 1 or 0.So one has to introduce the charge conjugate

*antiparticle*field, with its own creation and annihilation operators satisfying the relationswhere

*k*has the same*p*, and opposite σ and sign of the energy. Then one can rewrite the field in the formwhere the first sum is over positive energy states and the second over those of negative energy. The energy becomes

where

*E*is an infinite negative constant. The vacuum state_{0}Vacuum state

In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...

is defined as the state with no particle or antiparticle,

*i.e.*, and . Then the energy of the vacuum is exactly*E*. Since all energies are measured relative to the vacuum,_{0}**H**is positive definite. Analysis of the properties of*a*and_{k}*b*shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of a fermion_{k}Fermion

In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

.

This approach is due to Vladimir Fock

Vladimir Fock

Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....

, Wendell Furry and Robert Oppenheimer

Robert Oppenheimer

Julius Robert Oppenheimer was an American theoretical physicist and professor of physics at the University of California, Berkeley. Along with Enrico Fermi, he is often called the "father of the atomic bomb" for his role in the Manhattan Project, the World War II project that developed the first...

. If one quantizes a real scalar field

Scalar field theory

In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field...

, then one finds that there is only one kind of annihilation operator; therefore, real scalar fields describe neutral bosons. Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.

### Feynman–Stueckelberg interpretation

By considering the propagation of the negative energy modes of the electron field backward in time, Ernst StueckelbergErnst Stueckelberg

Ernst Carl Gerlach Stueckelberg was a Swiss mathematician and physicist.- Career :In 1927 Stueckelberg got his Ph. D. at the University of Basel under August Hagenbach...

reached a pictorial understanding of the fact that the particle and antiparticle have equal mass

**m**and spin**J**but opposite charges**q**. This allowed him to rewrite perturbation theoryPerturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an...

precisely in the form of diagrams. Richard Feynman

Richard Feynman

Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

later gave an independent systematic derivation of these diagrams from a particle formalism, and they are now called Feynman diagram

Feynman diagram

Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...

s. Each line of a diagram represents a particle propagating either backward or forward in time. This technique is the most widespread method of computing amplitudes in quantum field theory today.

Since this picture was first developed by Ernst Stueckelberg

Ernst Stueckelberg

Ernst Carl Gerlach Stueckelberg was a Swiss mathematician and physicist.- Career :In 1927 Stueckelberg got his Ph. D. at the University of Basel under August Hagenbach...

, and acquired its modern form in Feynman's work, it is called the

*Feynman-Stueckelberg interpretation*of antiparticles to honor both scientists.## See also

- Gravitational interaction of antimatterGravitational interaction of antimatterThe gravitational interaction of antimatter with matter or antimatter has not been conclusively observed by physicists. While the overwhelming consensus among physicists is that antimatter will attract both matter and antimatter at the same rate that matter attracts matter, there is a strong...
- ParityParity (physics)In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

, charge conjugation and time reversal symmetry. - CP violationCP violationIn particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...

s and the baryon asymmetry of the universe. - Quantum field theoryQuantum field theory

and the list of particles - BaryogenesisBaryogenesisIn physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...