Journal of Mathematical Physics

Path space measure for the 3+1-dimensional Dirac equation in momentum space

Tõru Nakamura

Published Aug 1, 2000• 6 citations

Abstract

Nonstandard analysis is used to construct a measure over paths for the path integral solution to the Dirac equation in 3+1 dimension. Paths are considered in momentum space, because the Green function in the configuration space contains a derivative of δ function which keeps us from assigning a measure over paths. The solution is obtained not only as the standard part of a nonstandard path sum with respect to a nonstandard measure, but also as a standard path integral with respect to a standard measure extracted from the nonstandard one. The result is an extension of Gaveau’s work [B. Gaveau, J. Funct. Anal. 58, 310–319 (1984)].

DOI: 10.1063/1.533402

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