Classical and Fluctuating Paths in Spaces with Curvature and Torsion

Details Classical and Fluctuating Paths in Spaces with Curvature and Torsion Classical and Fluctuating Paths in Spaces with Curvature and Torsion

1996-06-03

arxiv.org/abs/quant-ph/9606001v2

Physics

Quantum Physics

Lecture presented at the 5th INTERNATIONAL CONFERENCE ON PATH INTEGRALS FROM meV TO MeV, Dubna, May 27-31, 1996 For more info,

Scientific paper

This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure evolved from well established methods in the theory of plastic deformations where crystals with defects are described mathematically by applying nonholonomic coordinate transformations to ideal crystals. In the context of time-sliced path integrals, there seems to exists a quantum equivalence principle which determines the measures of fluctating orbits in spaces with curvature and torsion. The nonholonomic transformations produce a nontrivial Jacobian in the path measure which in a curved space produces an additional term proportional to the curvature scalar canceling a similar term found earlier by DeWitt from a naive formulation of Feynman's time-sliced path integral. This cancelation is important in 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 indispensible for the process of bosonization, by which Fermi particles are redescribed in terms of Bose fields.

Affiliated with

Also associated with

No associations

Rating

Classical and Fluctuating Paths in Spaces with Curvature and Torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical and Fluctuating Paths in Spaces with Curvature and Torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical and Fluctuating Paths in Spaces with Curvature and Torsion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184736