Simple Applications of Generalized Functions in Theoretical Physics: The Case of Many–Body Perturbation Expansions

H. F. G. Keiter
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H. F. G. Keiter: Universität Dortmund, Institut für Physik

A chapter in Generalized Functions, Convergence Structures, and Their Applications, 1988, pp 47-55 from Springer

Abstract: Abstract Let Ĥ = Ĥ0 + $${\rm{\hat V}}$$ be a self-adjoint operator, bounded from below and defined on a Hilbert space, representing the Himiltonian of an interacting physical system, and Ĥ0 the one for a simpler system with known spectrum and eigenstates. Typically, physicists want to evaluate the (grand–) canonical partition function Tr exp(–βĤ), where β-1 > 0 is Boltzmann’s constant times temperature, and Tr stands for the trace, in powers of $${\rm{\hat V}}$$ . For a fixed power of $${\rm{\hat V}}$$ , the expansion is unique and consists of a sum of terms, interpreted as physical processes. An individual term can be calculated only if generalized functions are introduced. This is a somewhat arbitrary procedure, however. Different schemes are presented an partial summations of individual terms through all the orders of the expansion in $${\rm{\hat V}}$$ are discussed.

Date: 1988
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DOI: 10.1007/978-1-4613-1055-6_4

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