Functional Schroedinger Equation for Fermions in External Gauge Fields

TL;DR

This paper develops the functional Schrödinger formalism for fermions in external gauge fields, providing explicit solutions and results for ground states, particle creation, and expectation values in various dimensions and models, including QED and non-abelian fields.

Contribution

It offers a comprehensive treatment of the functional Schrödinger picture for fermions in external fields, with explicit solutions in two and four dimensions, and discusses particle creation and gauge constraints.

Findings

Explicit ground state functionals for Schwinger models

Particle creation rates in constant external fields

Expectation values of charge and energy in various models

Abstract

We discuss the functional Schroedinger picture for fermions in external fields for both stationary and time-dependent problems. We give formal results for the ground state and the solution of the time-dependent Schroedinger equation for QED in arbitrary dimensions, while more explicit results are obtained in two dimensions. For both the massless and massive Schwinger model we give an explicit expression for the ground state functional as well as for the expectation values of energy, electric and axial charge. We also give the corresponding results for non-abelian fields. We solve the functional Schroedinger equation for a constant external field in four dimensions and obtain the amount of particle creation. We solve the Schroedinger equation for arbitrary external fields for massless QED in two dimensions and make a careful discussionof the anomalous particle creation rate. Finally, we discuss some subtleties connected with the interpretation of the quantized Gauss constraint.