Barry Martin Simon (Nova Iorque, 16 de abril de 1946) é um físico matemático estadunidense, professor de matemática e física teórica do Instituto de Tecnologia da Califórnia.
Foi palestrante convidado do Congresso Internacional de Matemáticos em Vancouver (1974: Approximation of Feynman Integrals and Markov fields by spin systems). Recebeu o Prêmio Henri Poincaré de 2012 e o Prêmio Bolyai de 2015. É desde 2013 fellow da American Mathematical Society e desde 1981 da American Physical Society. Em 2016 recebeu o Prêmio Leroy P. Steele por sua carreira, e o Prêmio Dannie Heineman de Física Matemática de 2018.
Em 1990 foi eleito membro correspondente da Academia Austríaca de Ciências. É fellow da Academia de Artes e Ciências dos Estados Unidos (2005).
Quantum theory of Hamiltonians defined by quadratic forms. Princeton 1971
Euclidean Quantum Field Theory. Princeton 1974
Trace Ideals and their applications. Cambridge 1979, 2. Edição AMS 2005
Functional integration and quantum physics. Academic Press 1979, 2. Edição AMS Chelsea Publishing 2005
Convexity. An analytic viewpoint. Cambridge University Press 2011
Statistical mechanics of lattices gases. Volume 1, Princeton 1993
com Michael C. Reed: Methods of Modern Mathematical Physics. Bd.1: Functional Analysis. Academic Press, 1972, 2. Auflage 1980; Volume 2: Fourier Analysis, Self-Adjointness. Academic Press, 1975; Volume 3: Scattering Theory. Academic Press, 1978; Volume 4: Analysis of Operators. Academic Press, 1977
com H. Cycon, R. Froese, W. Kirsch: Schrödinger Operators. Springer 1987, 2. Edição 2008, ISBN 978-3-540-16758-7.
Orthogonal polynomials on the unit circle, 2 Volumes, AMS Colloquium publications 2005
Editor com Lieb, Wightman: Studies in mathematical physics. Princeton 1976 (Bargmann-Festschrift), e por Simon: On the number of bound states of two body Schrödinger operators, a review e Quantum dynamics: from automorphism to hamiltonian.
Szegö´s theorem and its descendants. Spectral theory for
perturbations of orthogonal polynomials, Princeton University Press 2011
A comprehensive course in analysis, 5 Volumes, AMS 2015
Volume 1: Real analysis, Volume 2 A: Basic complex analysis, Volume 2 B: Advanced complex analysis, Volume 3: Harmonic analysis, Volume 4: Operator Theory
Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Math. 97 (1973), 247-274