Geodesic
Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 209-230

Voir la notice de l'article provenant de la source Math-Net.Ru

We compare different approaches to the construction of the quantum mechanics of a particle in the general Riemannian space and space-time via quantization of motion along geodesic lines. We briefly review different quantization formalisms and the difficulties arising in their application to geodesic motion in a Riemannian configuration space. We then consider canonical, semiclassical (Pauli–De Witt), and Feynman (path-integral) formalisms in more detail and compare the quantum Hamiltonians of a particle arising in these models in the case of a static, topological elementary Riemannian configuration space. This allows selecting a unique ordering rule for the coordinate and momentum operators in the canonical formalism and a unique definition of the path integral that eliminates a part of the arbitrariness involved in the construction of the quantum mechanics of a particle in the Riemannian space. We also propose a geometric explanation of another main problem in quantization, the noninvariance of the quantum Hamiltonian and the path integral under configuration space diffeomorphisms.
Keywords: quantum mechanics, Riemannian space, geodesic motion.
Mots-clés : quantization 
@article{TMF_2003_136_2_a2,
     author = {\'E. A. Tagirov},
     title = {Quantum {Mechanics} in {Riemannian} {Space:} {Different} {Approaches} to {Quantization} of the {Geodesic} {Motion} {Compared}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {209--230},
     publisher = {mathdoc},
     volume = {136},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a2/}
}
TY  - JOUR
AU  - É. A. Tagirov
TI  - Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 209
EP  - 230
VL  - 136
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a2/
LA  - ru
ID  - TMF_2003_136_2_a2
ER  - 
%0 Journal Article
%A É. A. Tagirov
%T Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 209-230
%V 136
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a2/
%G ru
%F TMF_2003_136_2_a2
É. A. Tagirov. Quantum Mechanics in Riemannian Space: Different Approaches to Quantization of the Geodesic Motion Compared. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 209-230. http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a2/