Stanley Mandelstam
Encyclopedia
Stanley Mandelstam is a South Africa
n-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables
into particle physics
in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a
central tool in the bootstrap program
which sought to formulate a consistent theory of infinitely many particle types of increasing spin.
Mandelstam, along with Tullio Regge
, was responsible for the Regge theory
of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes at high energy. Along with the double dispersion relation, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infintely many particle types, none of which are fundamental.
After Veneziano
constructed the first tree-level scattering amplitude describing infinitely many particle types, what was recognized almost immediately as a string scattering amplitude
, Mandelstam continued to make crucial contributions. He interpreted the Virasoro algebra
discovered in consistency conditions as a geometrical symmetry of a world-sheet conformal field theory, formulating string theory in terms of two dimensional quantum field theory. He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion scattering amplitudes in the Ramond
and Neveu-Schwarz sector
s of superstring theory, and later gave arguments for the finiteness of string perturbation theory.
Mandelstam has stated that he has not proved that string theory is finite and that he proved merely that a certain type of infinite term does not appear in string theory.
In quantum field theory, Mandelstam and independently Sidney Coleman
extended work of Tony Skyrme
to show that the two dimensional quantum Sine-Gordon model
is equivalently described by a Thirring model
whose fermions are the kinks. He also demonstrated that
the 4d N=4 supersymmetric gauge theory is power counting finite, proving that this theory is scale invariant to all orders of perturbation theory, the first example of a field theory where all the infinities in Feynman diagram
s cancel.
Among his students at Berkeley
are Joseph Polchinski
and Charles Thorn
.
Education: Witwatersrand
(BSc, 1952); Trinity College, Cambridge
(BA, 1954); Birmingham University (PhD, 1956).
South Africa
The Republic of South Africa is a country in southern Africa. Located at the southern tip of Africa, it is divided into nine provinces, with of coastline on the Atlantic and Indian oceans...
n-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables
Mandelstam variables
In theoretical physics, the Mandelstam variables are numerical quantities that encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion...
into particle physics
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...
in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a
central tool in the bootstrap program
Bootstrap model
In physics, the term bootstrap model is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles...
which sought to formulate a consistent theory of infinitely many particle types of increasing spin.
Mandelstam, along with Tullio Regge
Tullio Regge
Tullio Regge is an Italian theoretical physicist. He obtained a degree in physics from the University of Turin in 1952, and a Ph.D. in physics from the University of Rochester in 1957 under the direction of Robert Marshak. From 1958 to 1959 Regge held a post at the Max Planck Institute for...
, was responsible for the Regge theory
Regge theory
In quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer but is allowed to take any complex value...
of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes at high energy. Along with the double dispersion relation, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infintely many particle types, none of which are fundamental.
After Veneziano
Gabriele Veneziano
Gabriele Veneziano, born in Florence, Italy), is an Italian theoretical physicist and the founder of string theory. . Has spent most of his scientific activities at CERN in Geneva, Switzerland...
constructed the first tree-level scattering amplitude describing infinitely many particle types, what was recognized almost immediately as a string scattering amplitude
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, Mandelstam continued to make crucial contributions. He interpreted the Virasoro algebra
Virasoro algebra
In mathematics, the Virasoro algebra is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in conformal field theory and string theory....
discovered in consistency conditions as a geometrical symmetry of a world-sheet conformal field theory, formulating string theory in terms of two dimensional quantum field theory. He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion scattering amplitudes in the Ramond
Pierre Ramond
Pierre Ramond is a Distinguished Professor of Physics at University of Florida in Gainesville, Florida...
and Neveu-Schwarz sector
Neveu-Schwarz sector
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra and the Neveu–Schwarz algebra...
s of superstring theory, and later gave arguments for the finiteness of string perturbation theory.
Mandelstam has stated that he has not proved that string theory is finite and that he proved merely that a certain type of infinite term does not appear in string theory.
In quantum field theory, Mandelstam and independently Sidney Coleman
Sidney Coleman
Sidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann.- Life and work :Sidney Coleman grew up on the Far North Side of Chicago...
extended work of Tony Skyrme
Tony Skyrme
Tony Hilton Royle Skyrme, was a British physicist. He first proposed modeling the effective interaction between nucleons in nuclei by a zero-range potential, an idea still widely used today in nuclear structure and in equation of state for neutron stars. However, he is best known for formulating...
to show that the two dimensional quantum Sine-Gordon model
Sine-Gordon equation
The sine–Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. It was originally considered in the nineteenth century in the course of study of surfaces of constant negative...
is equivalently described by a Thirring model
Thirring model
The Thirring model is an exactly solvable quantum field theory which describes the self-interactions of a Dirac field in two dimension.-Definition:The Thirring model is given by the Lagrangian density...
whose fermions are the kinks. He also demonstrated that
the 4d N=4 supersymmetric gauge theory is power counting finite, proving that this theory is scale invariant to all orders of perturbation theory, the first example of a field theory where all the infinities in 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 cancel.
Among his students at 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...
are Joseph Polchinski
Joseph Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
and Charles Thorn
Charles Thorn
Charles Thorn is a Professor of Physics at University of Florida in Gainesville, Florida. He played an important role in the development of Dual Models and string theory. Among his contributions is the proof of the non-existence of ghosts in string theory. The Goddard–Thorn theorem is a...
.
Education: Witwatersrand
University of the Witwatersrand
The University of the Witwatersrand, Johannesburg is a South African university situated in the northern areas of central Johannesburg. It is more commonly known as Wits University...
(BSc, 1952); Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
(BA, 1954); Birmingham University (PhD, 1956).
Career
- Professor of Mathematical Physics, University of BirminghamUniversity of BirminghamThe University of Birmingham is a British Redbrick university located in the city of Birmingham, England. It received its royal charter in 1900 as a successor to Birmingham Medical School and Mason Science College . Birmingham was the first Redbrick university to gain a charter and thus...
, 1960-63 - Professeur Associé, Université de Paris-Sud, 1979-80 and 1984-85
- Professor of Physics, University of California, BerkeleyUniversity of California, BerkeleyThe University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, since 1963 (Professor Emeritus since 1994)
Honours
- Fellow of the Royal SocietyRoyal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, 1962 - DiracPaul DiracPaul 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...
Medal and Prize, International Centre for Theoretical PhysicsInternational Centre for Theoretical PhysicsThe Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...
, 1991 - Fellow, American Academy of Arts and SciencesAmerican Academy of Arts and SciencesThe American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
, 1992 - Dannie Heineman Prize for Mathematical PhysicsDannie Heineman Prize for Mathematical PhysicsDannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman...
, American Physical SocietyAmerican Physical SocietyThe American Physical Society is the world's second largest organization of physicists, behind the Deutsche Physikalische Gesellschaft. The Society publishes more than a dozen scientific journals, including the world renowned Physical Review and Physical Review Letters, and organizes more than 20...
, 1992