Nonequilibrium Problems in Quantum Field Theory and Schwinger’s Closed Time Path Formalism

Abstract

We review the closed time path formalism of Schwinger using a path integral approach. We apply this formalism to the study of pair production from strong external fields as well as the time evolution of a nonequilibrium chiral phase transition. In 1961 in his classic paper ``Brownian Motion of a Quantum Particle,`` Schwinger solved the formidable technical problem of how to use the action principle to study initial value problems. Previously, the action principle was formulated to study only transition matrix elements from an earlier time to a later time. The elegant solution of this problem was the invention of the closed time path (CTP) formalism. This formalism was first used to study field theory problems by Mahanthappa and Bakshi. With the advent of supercomputers, it has now become possible to use this formalism to numerically solve important field theory questions which are presented as initial value problems. Two of these problems we shall review here. They are (1) The time evolution of the quark- gluon plasma. (2) Dynamical evolution of a non-equilibrium chiral phase transition following a relativistic heavy ion collision.