Abstract
Reparametrization invariance treated as a gaugesymmetry shows some specific peculiarities. We studythese peculiarities both from a general point of viewand by concrete examples. We consider the canonical treatment of reparametrization-invariantsystems in which one fixes the gauge on the classicallevel by means of time-dependent gauge conditions. Insuch an approach one can interpret different gauges as different reference frames. We discuss therelation between different gauges and the problem ofgauge invariance in this case. Finally, we establish ageneral structure of reparametrizations and itsconnection with the zero-Hamiltonian phenomenon.
Similar content being viewed by others
REFERENCES
R. Arnowitt, S. Deser, and C. W. Misner, Phys. Rev. 116 (1959) 1322; 122 (1961) 997; iNuovo Cimento 19 (1961) 668; J. Math. Phys. 1 (1960) 434.
K. V. Kuchar, Phys. Rev. 34 (1986) 3031: D 39 (1989) 1579; J. Math. Phys. 23 (1982) 1647; P. Hajicek and K. V. Kuchar, Phys. Rev. D 41 (1990) 1091; P. Hajicek, Phys. Rev.D 38 (1988) 3639; J. Math. Phys. 30 (1989) 2488; Class. Quantum Grav. 13 (1996) 1353; Nucl. Phys. Proc. Suppl. 57 (1997) 115; J. B. Hartle and K. V. Kuchar, Phys. Rev. D 34 (1986) 2323; C. J. Isham and K. V. Kuchar, Ann. Phys. (NY) 164 (1985) 288, 316.
C. Isham, Canonical quantum gravity and the problem of time, Lectures presented at the NATO Advanced Study Institute, Salamanca, June 1992; gr-qc/9210011.
P. A. M. Dirac, Lectures on Quantum Mechanics, Yeshiva University Press, New York (1964).
D. M. Gitman and I. V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, Berlin (1990).
P. G. Bergmann, Introduction to the Theory of Relativity, Prentice-Hall, New York (1942).
J. M. Evans and Ph. A. Tuckey, Int. J. Mod. Phys. A 8 (1993) 4055; in Geomtry of Constrained Systems, Cambridge University Press, Cambridge (1994).
I. Batalin and S. L. Lyakhovich, in Group Theoretical Methods in Physics, Vol. 2, Nova Science, p. 57.
L. D. Landau and E. M. Lifshitz, Field Theory: Theoretical Physics, Vol. II, Nauka, Moscow (1973).
D. M. Gitman and I. V. Tyutin, JETP Lett. 51 (1990) 214; Class. Quantum Grav. 7 (1990) 2131.
S.-S. Feng and C.-G. Huang, Int. J. Theor. Phys. 36 (1997) 1179.
E. Noether, Nachr. Kgl. Ges. Wiss. Göttingen Math.-Phys. Kl. 2(1918) 235.
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press, Princeton, New Jersey, (1992).
P. A. M. Dirac, Proc. Roy. Soc. A 246 (1958) 326, 333.
L. D. Faddeev, Uspekhi Fiz. Nauk 136 (1982) 435.
Rights and permissions
About this article
Cite this article
Fulop, G., Gitman, D.M. & Tyutin, I.V. Reparametrization Invariance as Gauge Symmetry. International Journal of Theoretical Physics 38, 1941–1968 (1999). https://doi.org/10.1023/A:1026641400067
Issue Date:
DOI: https://doi.org/10.1023/A:1026641400067