München 1997 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP IX: HV IX

MP IX.1: Invited Talk

Wednesday, March 19, 1997, 14:00–14:45, HS 133

Quantum Equivalence Principle — •Hagen Kleinert — Freie Universit"at Berlin

A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. This procedure evolved from well-established methods in the theory of plastic deformations, where crystals with defects are described mathematically as images of ideal crystals under active nonholonomic coordinate transformations.

The mapping procedure may be viewed as a natural extension of Einsteins famous equivalence principle. When applied to time-sliced path integrals, it gives rise to a new quantum equivalence principle, determining short-time action and measure of fluctating orbits in spaces with curvature and torsion. The nonholonomic transformations possesses a nontrivial Jacobian in the path measure which produces in a curved space an additional term proportional to the curvature scalar canceling a similar term found earlier by DeWitt. This cancelation is important for correctly describing semiclassically and quantum mechanically various systems such as the hydrogen atom, a particle on the surface of a sphere, and a spinning top. It is also indispensable for the process of bosonization, by which Fermi particles are redescribed in terms of Bose fields.