Stanley Mandelstam

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Stanley Mandelstam
Born (1928-12-12)12 December 1928
Johannesburg,[1] South Africa
Died 11 June 2016(2016-06-11) (aged 87)
Berkeley, California, U.S.
Fields Particle physics
String theory
Institutions University of the Witwatersrand,
University of California - Berkeley,
University of Birmingham
Alma mater University of the Witwatersrand,
Birmingham University,
Trinity College, Cambridge
Thesis Some Contributions to the Theory and Application of the Bethe-Salpeter Equation (1956)
Doctoral advisor Richard Henry Dalitz
Other academic advisors Paul Taunton Matthews
Doctoral students Michio Kaku
Charles Thorn
Joseph Polchinski
Nathan Berkovits
Known for Double dispersion relations
Notable awards Dirac Medal
Dannie Heineman Prize for Mathematical Physics (1992)

Stanley Mandelstam (12 December 1928 – 23 June 2016) was a South Africa-born American 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.[2] 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, did the initial development of 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 relations, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infinitely 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 sectors of superstring theory, and later gave arguments for the finiteness of string perturbation 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 diagrams cancel.

Among his students at Berkeley are Joseph Polchinski, Michio Kaku, Charles Thorn and Nathan Berkovits.

Stanley Mandelstam died in his Berkeley apartment in June, 2016.





  1. ^ Array of Contemporary American Physicists
  2. ^ Mandelstam, S. (1958). "Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity general theory." Physical Review. 112(4), 1344–1360.

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