60,185 research outputs found
Path integral representation of the evolution operator for the Dirac equation
A path integral representation of the evolution operator for the
four-dimensional Dirac equation is proposed. A quadratic form of the canonical
momenta regularizes the original representation of the path integral in the
electron phase space. This regularization allows to obtain a representation of
the path integral over trajectories in the configuration space, i.e. in the
Minkowsky space. This form of the path integral is useful for the formulation
of perturbation theory in an external electromagnetic field.Comment: 3 page
Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space
Path integral formulations for the Smorodinsky-Winternitz potentials in two-
and three-dimen\-sional Euclidean space are presented. We mention all
coordinate systems which separate the Smorodinsky-Winternitz potentials and
state the corresponding path integral formulations. Whereas in many coordinate
systems an explicit path integral formulation is not possible, we list in all
soluble cases the path integral evaluations explicitly in terms of the
propagators and the spectral expansions into the wave-functions.Comment: LaTeX 60 pages, DESY 94-01
Bergman Kernel from Path Integral
We rederive the expansion of the Bergman kernel on Kahler manifolds developed
by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation
theory, and generalize it to supersymmetric quantum mechanics. One physics
interpretation of this result is as an expansion of the projector of wave
functions on the lowest Landau level, in the special case that the magnetic
field is proportional to the Kahler form. This is relevant for the quantum Hall
effect in curved space, and for its higher dimensional generalizations. Other
applications include the theory of coherent states, the study of balanced
metrics, noncommutative field theory, and a conjecture on metrics in black hole
backgrounds. We give a short overview of these various topics. From a
conceptual point of view, this expansion is noteworthy as it is a geometric
expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time
expansion for the heat kernel, but in this case describing the long time limit,
without depending on supersymmetry.Comment: 27 page
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