Vaclav Zatloukal (Czech Technical University, Prague)

Local-time representation of path integrals

We derive a local-time path-integral representation of one-dimensional time-independent quantum-mechanical systems. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman–Kac formula, particularly in the low temperature regimes.