Spurion
Encyclopedia
In theoretical physics
, a spurion is a fictitious, auxiliary field in a quantum field theory
that can be used to parameterize any symmetry breaking
and to determine all operator
s invariant under the symmetry.
The procedure begins with finding a parameter that measures the amount of symmetry breaking. This parameter is promoted to a field, i.e. to a function of the spacetime coordinates. With this new fictitious field, operators that are invariant under the symmetry may be found by the usual group-theoretical considerations.
The list of operators found in this way is complete as long as all sources of the breaking are included. The operators in the actual theory are ultimately found by setting the spurious field equal to the constant value of the parameter.
s, physics often uses the chiral perturbation theory
. Here, the relevant symmetry is the isospin
SU(2) symmetry. It is broken by the different masses of the u and d quark
s as well as by their different charges. The chiral Lagrangian may be extended to an exactly SU(2)-symmetric Lagrangian by promoting these parameters (mass and charge) to fields that break the symmetry spontaneously. Calculations of observables to higher orders may be done with the spurion fields. The final result, at any order of accuracy, are obtained by substituting the right masses and charges.
In the standard electroweak theory, the spurion is replaced by an actual field, the Higgs boson
. However, in alternative theories of electroweak symmetry breaking, e.g. those based on technicolor
, the spurion techniques are important to derive the physical predictions.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, a spurion is a fictitious, auxiliary field in 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...
that can be used to parameterize any symmetry breaking
Symmetry breaking
Symmetry breaking in physics describes a phenomenon where small fluctuations acting on a system which is crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations , the choice will appear arbitrary...
and to determine all operator
Operator (physics)
In physics, an operator is a function acting on the space of physical states. As a resultof its application on a physical state, another physical state is obtained, very often along withsome extra relevant information....
s invariant under the symmetry.
The procedure begins with finding a parameter that measures the amount of symmetry breaking. This parameter is promoted to a field, i.e. to a function of the spacetime coordinates. With this new fictitious field, operators that are invariant under the symmetry may be found by the usual group-theoretical considerations.
The list of operators found in this way is complete as long as all sources of the breaking are included. The operators in the actual theory are ultimately found by setting the spurious field equal to the constant value of the parameter.
Applications
In the theory of pionPion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s, physics often uses the chiral perturbation theory
Chiral perturbation theory
Chiral perturbation theory is an effective field theory constructed with a Lagrangian consistent with the chiral symmetry of quantum chromodynamics , as well as the other symmetries of parity and charge conjugation. ChPT is a theory which allows one to study the low-energy dynamics of QCD...
. Here, the relevant symmetry is the isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
SU(2) symmetry. It is broken by the different masses of the u and d quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s as well as by their different charges. The chiral Lagrangian may be extended to an exactly SU(2)-symmetric Lagrangian by promoting these parameters (mass and charge) to fields that break the symmetry spontaneously. Calculations of observables to higher orders may be done with the spurion fields. The final result, at any order of accuracy, are obtained by substituting the right masses and charges.
In the standard electroweak theory, the spurion is replaced by an actual field, the Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
. However, in alternative theories of electroweak symmetry breaking, e.g. those based on technicolor
Technicolor (physics)
Technicolor theories are models of physics beyond the standard model that address electroweak symmetry breaking, the mechanism through which elementary particles acquire masses...
, the spurion techniques are important to derive the physical predictions.