Physics – Quantum Physics
Scientific paper
1995-11-18
in Proceedings of the XXV International Symposium Ahrenshoop on Theory of Elementary Particles in Gosen/Germany 1991, ed. by H
Physics
Quantum Physics
Scientific paper
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.
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