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Journal of Mathematical Physics

A model of field theory treated in the Fock-Cook formalism

Franklin E. Schroeck

Published Jan 1, 1973• 4 citations
Publisher

Abstract

We present an alternative to the usual formalism for quantum field theory by generalizing the Fock-Cook formalism. We illustrate the method by applying it to a generalization of a familiar model of quantum field theory.
DOI
10.1063/1.1666163

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The formalism of the second quantization is developed entirely within the framework of the Dirac-Jordan representation theory. The equivalence of this formalism and the methods of ordinary coordinate-spin space is shown, and the equations of "connection" are fully developed. It is shown that the "creation" and "annihilation" operators, and indeed all operators which do not commute with the quantized Hamiltonian and hence whose representatives cannot be explicitly given in a configuration space of a fixed number of dimensions are easily treated in terms of the general representation theory and arise quite naturally. Both types of statistics are considered, and the Fock-Dirac density matrix and self-consistent field are treated as a simple illustration.