Local-time representation of path integrals.

摘要: We derive a local-time path-integral representation for generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of Bloch density as path integral over x-dependent profiles. The latter quantify time that sample paths x(t) in Feynman spend vicinity an arbitrary point x. Generalization includes functionals local is also provided. argue results obtained represent powerful alternative traditional Feynman-Kac formula, particularly high- and low-temperature regimes. To illustrate this point, apply our analyze asymptotic behavior at low temperatures. Further salient issues, such connections with Sturm-Liouville theory Rayleigh-Ritz variational principle, are discussed.