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
Hessamaddin Arfaei. Stanley Mandelstam died in his
Berkeley apartment in June, 2016. ==Education==