Abstract:
The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.). © 1992 The American Physical Society.
Referencias:
- Teitelboim, C., (1982) Phys. Rev. D, 25, p. 3159
- Henneaux, M., Teitelboim, C., (1982) Ann. Phys. (N.Y.), 143, p. 127
- Halliwell, J.J., (1988) Phys. Rev. D, 38, p. 2468
- Dirac, P.A.M., (1964) Lectures on Quantum Mechanics, Belfer Graduate School of Science, , Yeshiva University, New York
- Hartle, J.B., Kuchař, K., (1986) Phys. Rev. D, 34, p. 2323
- Faddeev, L.D., Slavnov, A.A., (1980) Gauge Fields: Introduction to Quantum Theory, , Benjamin/Cummings, Reading, MA
- Lee, T.D., (1981) Particle Physics and Introduction to Field Theory, , Harwood, New York
- Kuchař, K., (1983) J. Math. Phys., 24, p. 2122
- When the Hamiltonian is quadratic in the momenta, the function B is not relevant because no track of B remains after the integration on the momenta; however, B is not necessarily the only kind of ambiguity the skeletonization can have [7]; Feynman, R.P., Hibbs, A.R., (1965) Quantum Mechanics and Path Integrals, , McGraw-Hill, New York
- Newton, T.D., Wigner, E.P., (1949) Rev. Mod. Phys., 21, p. 400
- J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1960); in Relativity, Groups and Topology, Proceedings of the Summer School of Theoretical Physics, Grenoble, France, 1963, edited by C. DeWitt and B. DeWitt (Gordon and Breach, London, 1964); This also implies that the quantum propagator does not vanish for nonsimultaneous points with spacelike separation. However, the probability of finding the particle at a point x prime prime outside of the light cone of x prime quickly goes to zero for (imaginary) geodesic distances such that | sqrt {2 σ} | is larger than the Compton wavelength of the particle; Birrell, N.D., Davies, P.C.W., (1982) Quantum Fields in Curved Space, , Cambridge University Press, Cambridge, England
- Misner, C.W., Thorne, K.S., Wheeler, J.A., (1973) Gravitation, , Freeman, San Francisco
- The exponent 1/(2-D) is dictated by the gauge condition for the perturbation of the flat metric. In the case D=2 the gauge condition does not fix the exponent, but imposes a restriction on PHI
Citas:
---------- APA ----------
(1992)
. Path integral for the relativistic particle in curved space. Physical Review D, 45(4), 1198-1209.
http://dx.doi.org/10.1103/PhysRevD.45.1198---------- CHICAGO ----------
Ferraro, R.
"Path integral for the relativistic particle in curved space"
. Physical Review D 45, no. 4
(1992) : 1198-1209.
http://dx.doi.org/10.1103/PhysRevD.45.1198---------- MLA ----------
Ferraro, R.
"Path integral for the relativistic particle in curved space"
. Physical Review D, vol. 45, no. 4, 1992, pp. 1198-1209.
http://dx.doi.org/10.1103/PhysRevD.45.1198---------- VANCOUVER ----------
Ferraro, R. Path integral for the relativistic particle in curved space. 1992;45(4):1198-1209.
http://dx.doi.org/10.1103/PhysRevD.45.1198