Geodesic
Path integrals and ordering of operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 51-63

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

A method, not based on finite-multiplicity approximations, is proposed for constructing the Feynman path integral for a particle in a curved space whose geometry is defined by the kinetic energy. For the example of a system with the Hamiltonian $H=f^2(x)p^2$ (and some other systems) it is shown that the path integral can be obtained by a change of the variables of integration from a Gaussian functional integral, and this then makes it possible to associate the function $H$ uniquely with an operator. The procedure for constructing the operator corresponding to a classical function of the coordinates and the momenta, for given form of the Hamiltonian, is also considered. 
@article{TMF_1979_40_1_a5,
     author = {L. F. Blazhievskii},
     title = {Path integrals and ordering of operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {51--63},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a5/}
}
TY  - JOUR
AU  - L. F. Blazhievskii
TI  - Path integrals and ordering of operators
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 51
EP  - 63
VL  - 40
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a5/
LA  - ru
ID  - TMF_1979_40_1_a5
ER  - 
%0 Journal Article
%A L. F. Blazhievskii
%T Path integrals and ordering of operators
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 51-63
%V 40
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a5/
%G ru
%F TMF_1979_40_1_a5
L. F. Blazhievskii. Path integrals and ordering of operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 51-63. http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a5/