Sum-over-histories representation for the causal Green function of free scalar field theory

الأصل · EN

A set of Green functions Gα(x-y), α∈ [0, 2 π[, for free scalar field theory is introduced, varying between the Hadamard Green function Δ₁(x-y) ≡ [2] 0 -0.1cm { φ(x), φ(y) } -0.1cm 0 and the causal Green function Gπ(x-y) = i Δ(x-y) ≡ [φ(x), φ(y)]. For every α∈ [0, 2 π[a path-integral representation for Gα is obtained both in the configuration space and in the phase space of the classical relativistic particle. Especially setting α= π a sum-over-histories representation for the causal Green function is obtained. Furthermore using BRST theory an alternative path-integral representation for Gα is presented. From these path integral representations the composition laws for the Gα's are derived using a modified path decomposition expansion.