Freeman J. Dyson

TL;DR: In this article, three kinds of statistical ensembles are defined, representing a mathematical idealization of the notion of ''all physical systems with equal probability'' and three groups are studied in detail, based mathematically upon the orthogonal, unitary and symplectic groups.

TL;DR: In this paper, a new type of Coulomb gas is defined, consisting of n point charges executing Brownian motions under the influence of their mutual electrostatic repulsions, and it is proved that this gas gives an exact mathematical description of the behavior of the eigenvalues of an (n × n) Hermitian matrix, when the elements of the matrix execute independent Brownian motion without mutual interaction.

Abstract: The covariant quantum electrodynamics of Tomonaga, Schwinger, and Feynman is used as the basis for a general treatment of scattering problems involving electrons, positrons, and photons. Scattering processes, including the creation and annihilation of particles, are completely described by the $S$ matrix of Heisenberg. It is shown that the elements of this matrix can be calculated, by a consistent use of perturbation theory, to any desired order in the fine-structure constant. Detailed rules are given for carrying out such calculations, and it is shown that divergences arising from higher order radiative corrections can be removed from the $S$ matrix by a consistent use of the ideas of mass and charge renormalization.Not considered in this paper are the problems of extending the treatment to include bound-state phenomena, and of proving the convergence of the theory as the order of perturbation itself tends to infinity.

TL;DR: In this paper, an ideal model of a ferromagnet is studied, consisting of a lattice of identical spins with cubic symmetry and with isotropic exchange coupling between nearest neighbors.

TL;DR: In this article, a unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory.