title: Local-time representation of path integrals.
abstract: We derive a local-time path-integral representation for a generic one-dimensional time-independent system. 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 high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
authors.affiliation: ITP, Freie Universität in Berlin, Arnimallee 14, D-14195 Berlin, Germany;  2. FNSPE, Czech Technical University in Prague, Bˇrehov´a 7, 115 19 Praha 1, Czech Republic.|FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic.
authors.forename: Petr
authors.initials: P
authors.lastname: Jizba
authors.affiliation: FNSPE, Czech Technical University in Prague, Bˇrehov´a 7, 115 19 Praha 1, Czech Republic; 2. Max Planck Institute for the History of Science, Boltzmannstrasse 22, D-14195 Berlin, Germany.
authors.forename: Václav
authors.initials: V
authors.lastname: Zatloukal