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| related topics |
| {phase, path, phys} |
| {equation, function, exp} |
| {group, space, representation} |
| {field, particle, equation} |
| {force, casimir, field} |
| {cos, sin, state} |
| {theory, mechanics, state} |
|
Quantum Equivalence Principle for Path Integrals in Spaces with
Curvature and Torsion
H. Kleinert
abstract: We formulate a new quantum equivalence principle by which a path integral for
a particle in a general metric-affine space is obtained from that in a flat
space by a non-holonomic coordinate transformation. The new path integral is
free of the ambiguities of earlier proposals and the ensuing Schr\"odinger
equation does not contain the often-found but physically false terms
proportional to the scalar curvature. There is no more quantum ordering
problem. For a particle on the surface of a sphere in $D$ dimensions, the new
path integral gives the correct energy $\propto \hat L^2$ where $\hat L$ are
the generators of the rotation group in ${\bf x}$-space. For the transformation
of the Coulomb path integral to a harmonic oscillator, which passes at an
intermediate stage a space with torsion, the new path integral renders the
correct energy spectrum with no unwanted time-slicing corrections.
- oai_identifier:
- oai:arXiv.org:quant-ph/9511020
- categories:
- quant-ph
- arxiv_id:
- quant-ph/9511020
- journal_ref:
- in Proceedings of the XXV International Symposium Ahrenshoop on
Theory of Elementary Particles in Gosen/Germany 1991, ed. by H. J. Kaiser
- created:
- 1995-11-18
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