Sum-over-histories representation for the causal Green function of free scalar field theory
- II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
A set of Green functions [ital scrG][sub [alpha]]([ital x][minus][ital y]), [alpha][element of][0,2[pi]] for free scalar field theory is introduced, varying between the Hadamard Green function [Delta][sub 1]([ital x][minus][ital y])==[l angle]0[vert bar][l brace][ital cphi]([ital x]),[ital cphi]([ital y])[r brace][vert bar]0[r angle] and the causal Green function [ital scrG][sub [pi]]([ital x][minus][ital y])=[ital i][Delta]([ital x][minus][ital y])==[[ital cphi]([ital x]),[ital cphi]([ital y])]. For every [alpha][element of][0,2[pi]] a path integral representation for [ital scrG][sub [alpha]] is obtained both in configuration space and in the phase space of the classical relativistic particle. Setting [alpha]=[pi] a sum-over-histories representation for the causal Green function is obtained. Furthermore, a reduced phase space integral representation for the [ital scrG][sub [alpha]]'s is stated and an alternative BRST path integral representation for [ital scrG][sub [alpha]] is presented. From these path integral representations the composition laws for the [ital scrG][sub [alpha]]'s are derived using a modified path decomposition expansion.
- OSTI ID:
- 6579309
- Journal Information:
- Physical Review, D (Particles Fields); (United States), Vol. 51:4; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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