An Operator Derivation of the Path Decomposition Expansion

Details An Operator Derivation of the Path Decomposition Expansion An Operator Derivation of the Path Decomposition Expansion

1995-06-14

arxiv.org/abs/quant-ph/9506021v1

Phys. Lett. A207:237-242,1995

Physics

Quantum Physics

9 pages Plain Tex

Scientific paper

10.1016/0375-9601(95)00703-6

The path decomposition expansion is a path integral technique for decomposing sums over paths in configuration space into sums over paths in different spatial regions. It leads to a decomposition of the configuration space propagator across arbitrary surfaces in configuration space. It may be used, for example, in calculations of the distribution of first crossing times. The original proof relied heavily on the position representation and in particular on the properties of path integrals. In this paper, an elementary proof of the path decomposition expansion is given using projection operators. This leads to a version of the path decomposition expansion more general than the configuration space form previously given. The path decomposition expansion in momentum space is given as an example.

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