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Journal of Mathematical Physics

Expectation Value Formalism in Quantum Field Theory. II

Pradip M. Bakshi, Kalyana T. Mahanthappa

Published Jan 1, 1963• 372 citations
Publisher

Abstract

The expectation value formalism has been developed to treat the problems which require the coupling of quantized Fermi and Bose fields.
DOI
10.1063/1.1703879

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Expectation value of composite field TTˉT{\bar T}TTˉ in two-dimensional quantum field theory
I show that the expectation value of the composite field TTˉT{\bar T}TTˉ, built from the components of the energy-momentum tensor, is expressed exactly through the expectation value of the energy-momentum tensor itself. The relation is derived in two-dimensional quantum field theory under broad assumptions, and does not require integrability.
We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anticommutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anticommutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
The partition function of the ferroelectric problem is expressed as a vacuum-to-vacuum expectation value of a time-ordered product of Fermi operators. The expression obtained is typical of those that arise in treating interacting Fermi systems. Apart from evaluating the critical temperature as a function of the electric field, we have not been able to obtain Lieb's exact solution from this formalism. However, the first-order approximation is found to be closely related to Lieb's solution, giving some of the critical behavior correctly.