«For contributions to the theory of elementary particles, nuclei and condensed matter, especially his courage and persistence in deriving the properties of nuclear matter from nucleon-nucleon interactions»
«For several outstanding achievements in bringing the resources of modern mathematics to bear upon fundamental problems of physics, and in particular for the first rigorous proof of dispersion relations for the non-forward scattering of elementary particles»
«For contributions to quantum field theory, for his investigation of the theory of scattering of particles with spin, and his recent deep analysis of the symmetry principles in physics»
«For his development of superconvergence relations and their applications to fundamental problems of elementary particle physics, as examples of outstanding publication in the field of mathematical physics»
«For his diverse and profound contributions to theory, specifically for analysis of symmetry breaking into particle physics and of gauge invariance in the BCS theory of superconductivity, as examples of mathematical physics»
«For his contribution to general relativity including new mathematical techniques, new conservation laws and his theorem on singularities in space-time, each represented by an outstanding publication in the field of Mathematical Physics»
«For his contributions to particle theory, in particular his elucidation of the connection between the short distance behavior of current and such physical phenomena as inelastic lepton scattering -- contributions that are examples of outstanding publication in the field of mathematical physics»
«For his work on the implications of broken scale invariance in quantum field theory and for his work on the scaling behavior of critical phenomena in statistical mechanics»
«For application of the elegant and rigorous techniques of mathematical physics to problems of stellar structure, radiative transfer, hydromagnetic stability, the post-Newtonian approximation in general relativity, and the stability off rotating, gravitating bodies, thus continuing and bringing up to date the tradition established by such mathematical physicists as Poincare and Lord Rayleigh»
«For his mathematically and physically incisive work on the three-body problem, and for his profound contribution to the quantization of gauge fields by the method of functional integration»
«For his discovery of remarkable features of gravitational singularities in General Relativity including the growth and the death of black holes and the universe all represented by outstanding publications in the field of mathematical physics»
«For his formulation of unified gauge theories of weak and electromagnetic interactions and his analysis of the role of spontaneous symmetry briefing in such theories, all represented by outstanding publications in the field of mathematical physics»
«For his contributions to statistical mechanics, especially for obtaining the exact solution to problems using two-dimensional ferroelectric models, and the decisive clarification of Coulomb interactions, all represented by outstanding publications in the field of mathematical physics»
«For his contributions to Quantum Field Theory, in particular for his studies of the renormalization and other features of Non-Abelian Gauge Theories, all represented by outstanding publications in the Field of Mathematical Physics»
«For their joint contributions to constructive quantum field theory; in particular for their solutions of models of interacting fields in two and three space-time dimensions, thereby demonstrating the compatibility of relativistic invariance, quantum mechanics, and local field theory»
«For his contribution to nuclear physics, condensed matter physics and to quantum field theory, in establishing the first rigorous diagrammatic technique for the many-body problem and in proving a fundamental theorem on spontaneously broken global symmetry»
«For his important contributions to general relativity, plasma physics and especially to the theory of some special nonlinear differential equations useful in many areas of physics»
«For his contribution to statistical mechanics and thermodynamics; in particular, for his work on correlation inequalities, the theory of tricritical points, and phases equilibria»
«For his systematic pursuit of the mathematical basis needed for broadened physical insight in the areas of quantum field theory, statistical mechanics and turbulence»
«For his contributions to Mathematical Physics by his analyses of topological effects in quantum field theory as pertains to statistical systems and elementary particles»
«For his novel use of mathematical analysis to solve in exact analytical form problems of fundamental importance in statistical mechanics relating directly to cooperative phenomena, phase transitions and quantum field theory»
«For crucial contributions to the discovery and development of supersymmetry, a profound extension of the notation of space-time symmetry, that may underlie unification of the fundamental forces»
«For his numerous incisive original contributions to quantum theory and elementary particle physics; in particular, for the Bell inequality, which has played a major role in theoretical and experimental work on the foundations of quantum mechanics»
«For his discoveries of new concepts and his proofs of deep mathematical theorems that have become central to our understanding of both dynamical systems and the foundations of statistical mechanics»
«For his fundamental contributions to elementary particle physics, including the Mandelstam representation, which displays the analyticity, properties of scattering amplitudes, the formulation of the relativistic string as a unitary theory of interacting particles, and his influential work on gauge theories»
«For his incisive studies of the semi-classical limit of quantum mechanics, and in particular his trace formula relating the quantum spectrum to periodic classical orbits»
«For their joint development of a canonical formalism for general relativity which clarified some important physical issues pertaining to gravity and laid the foundation for modern theoretical advancement in gravity and cosmology»
«For his imaginative use of quantum field theory to throw light on physical problems, including his work on topological solitons, field theory at high temperatures, the existence of anomalies, and the role of these anomalies in particle physics»
«For their decisive advances in elucidating the dynamics of strongly coupled supersymmetric field and string theories. The deep physical and mathematical consequences of the electric-magnetic duality they exploited have broadened the scope of Mathematical Physics»
«For incisive contributions to the development and understanding of modern theories of elementary particles. Of particular note are his contributions to symmetry breaking and the roles played by internal and space-time symmetries as well as the structure of solutions to an important model in quantum field theory»
«For his fundamental contributions to our understanding of dynamics and of singularities of maps with profound consequences for mechanics, astrophysics, statistical mechanics, hydrodynamics and optics»
«For separate as well as joint work in proving the existence and uniqueness of solutions to Einstein's gravitational field equations for a variety of sources, and for formulating these equations so as to improve numerical solution procedures with relevance to realistic physical systems»
«For his pioneering discoveries in dual resonance models which, partly through his own efforts, have developed into string theory and a basis for the quantum theory of gravity»
«For fundamental theoretical discoveries in broad areas of elementary particle physics, quantum field theory, and statistical mechanics; especially for work on spin glasses and disordered systems»
«For constructing supergravity, the first supersymmetric extension of Einstein's theory of general relativity, and for their central role in its subsequent development»
«For profound developments in Mathematical Physics that have illuminated interconnections and launched major research areas in Quantum Field Theory, String Theory, and Gravity»
«For developing the theory of deterministic chaos, especially the universal character of period doubling, and for the profound influence of these discoveries on our understanding of nonlinear phenomena in physics»
«For discovery and exploitation of the BRST symmetry for the quantization of gauge theories providing a fundamental and essential tool for subsequent developments»
«For his development of the random current approach to correlations which has had an impact on a wide variety of problems, especially his rigorous non-perturbative proof of the triviality of Æ4 field theory»
«For his seminal contributions to nonequilibrium statistical mechanics as exemplified by his exact solutions of growth models and stationary states of open systems. Combining mathematical rigor with physical insight his work elucidates the transition from microscopic to macroscopic behavior»
«For contributions to the interaction between statistical mechanics, field theory and the theory of elementary particles, including spontaneous symmetry breaking, critical phenomena and a general theory of dissipative systems»
«For profound developments in integrable systems and their correlation functions in statistical mechanics and quantum field theory, making use of quantum groups, algebraic analysis and deformation theory»
«For eminent contributions to mathematical physics with a wide influence in many fields, ranging from string theory to supersymmetric gauge theory, conformal field theory, condensed matter physics and four-manifold theory»
«For pioneering foundational discoveries in supersymmetry and superstring theory, in particular the dual model of fermions and the theory of the Kalb-Ramond field»
«For leadership in numerous central developments in string theory, quantum field theory, and quantum geometry; including the interplay between string theory and Calabi-Yau geometry and especially for their elucidation of the origin of black hole entropy from microscopic states»
«For developing the theory of PT symmetry in quantum systems and sustained seminal contributions that have generated profound and creative new mathematics, impacted broad areas of experimental physics, and inspired generations of mathematical physicists»
«For his fundamental contributions to the mathematical physics of quantum mechanics, quantum field theory, and statistical mechanics, including spectral theory, phase transitions, and geometric phases, and his many books and monographs that have deeply influenced generations of researchers»
«For profound contributions to the field of exactly solvable models in statistical mechanics and many body physics, in particular the construction of the widely studied Gaudin magnet and the Calogero-Sutherland, Shastry-Sutherland, and Calogero-Moser models»
«For work on the spectral theory of almost-periodic Schrödinger operators and related questions in dynamical systems. In particular, for her role in the solution of the Ten Martini problem, concerning the Cantor set nature of the spectrum of all almost Mathieu operators and in the development of the fundamental mathematical aspects of the localization and metal-insulator transition phenomena»
«For seminal contributions to nonequilibrium and equilibrium statistical mechanics, in particular, studies of large deviations in nonequilibrium steady states and rigorous analysis of Gibbs equilibrium ensembles»
«For fundamental contributions to quantum field theory, statistical mechanics, and fluid dynamics using geometric, probabilistic, and renormalization group ideas»
«For the elegant application of powerful mathematical techniques to extract exact results for quantum field theories, as well as shedding light on integrable systems and non-commutative geometry»
«For achievements in the fields of constructive quantum field theory and rigorous statistical mechanics, especially the introduction of new techniques including random walk representation in spin systems, the lace expansion, and mathematically rigorous implementations of the renormalization group»
«For clever use of various techniques in studying symmetry in quantum field theory, in particular, for work with L. Faddeev on anomalies, with C. Vafa on exceptional holonomy compactifications of superstrings, and for the co-discovery of Bethe/gauge correspondence between supersymmetric vacua and quantum integrability»
