Prog. Theor. Phys. Vol. 66 No. 2 (1981) pp. 672-684
Covariant Schrödinger Equation via Path Integrals
Department of Physics, Faculty of Engineering, Kanagawa University, Yokohama 221
(Received September 18, 1980)
Propagation equations of infinitesimal time differences in path integral representations are investigated in a manifestly covariant way in the curved space-time. Covariant Schrödinger equations via these path integrals are studied by using a formula which expresses explicitly the relation between normal coordinates and general covariant ones within the required approximation.
The Dirac equation is investigated by using the devices that we developed in our previous paper and the ambiguity in defining the normalization factor is removed.
Path integrals in phase space are discussed by applying such factor orderings as the geodesic distance approximation to the metric fields and the hermitian one to the gauge fields, which reduces the Hamiltonian formulations to the Lagrangian ones. The Kaluza-Klein theory is studied in the framework of path integrals as an example of the above investigations.
DOI : 10.1143/PTP.66.672
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Citing Article(s) :
Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 571-575
WKB Approximations for Relativistic Particles