Abstract
The relationship between the canonical operator and the path integral formulation of quantum electrodynamics is analyzed with a particular focus on the implementation of gauge constraints in the two approaches. The removal of gauge volumes in the path integral is shown to match with the presence of zero-norm ghost states associated with gauge transformations in the canonical operator approach. The path integrals for QED in both the Feynman and the temporal gauges are examined and several ways of implementing the gauge constraint integrations are demonstrated. The upshot is to show that both the Feynman and the temporal gauge path integrals are equivalent to the Coulomb gauge path integral, matching the results developed by Kurt Haller using the canonical formalism. In addition, the Faddeev–Popov form for the Feynman gauge and temporal gauge Lagrangian path integrals are derived from the Hamiltonian form of the path integral.
Similar content being viewed by others
REFERENCES
K. Haller, Acta Phys. Aust. 42, 163 (1975).
K. Haller, Phys. Rev. D 36, 1830 (1987).
K. Haller and E. Lim-Lombridas, Found. Phys. 24, 217 (1994).
M. Swanson, Phys. Rev. D 24, 2132 (1981).
L. D. Faddeev and V. N. Popov, Phys. Lett. B 25, 29 (1967).
C. Becchi, A. Rouet, and R. Stora, Ann. Phys. 98, 297 (1976). I. V. Tyupin, Lebedev Preprint, FIAN No. 39 (1975), unpublished.
I. Batalin and G. Vilkovisky, Phys. Rev. D 28, 2567 (1983).
M. Swanson, Path Integrals and Quantum Processes (Academic, New York, 1992).
A. A. Slavnov, Teoret. Mat. Fiz. 22, 177 (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Swanson, M.S. Of Ghosts, Gauge Volumes, and Gauss's Law. Foundations of Physics 30, 359–370 (2000). https://doi.org/10.1023/A:1003613621299
Issue Date:
DOI: https://doi.org/10.1023/A:1003613621299