Abstract
We introduce a ‘proper time’ formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field-theoretic problem to a quantum mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the Hamiltonian. We show that the ‘proper time’ unitary evolution splits into two semigroups. The semigroup associated with decaying Gamov vectors is related to the Feynman boundary conditions for the Green functions and the semigroup associated with growing Gamov vectors is related to the Dyson boundary conditions.
Similar content being viewed by others
References
Aghassi, J. J., Roman, P., and Santilli, R. M. (1970)Physical Review D,1, 2753.
Aparicio, J. P., Gaioli, F. H., and Garcia-Alvarez, E. T. (1995a).Physical Review A,51, 96.
Aparicio, J. P., Gaioli, F. H., and Garcia-Alvarez, E. T. (1995b).Physics Letters A,200, 233.
Bohm, A., Gadella, M., and Mainland, G. B. (1989).American Journal of Physics,57, 1103.
Bredov, M., Rumiántsev, V., and Toptiguin, I. (1984)Electrodinámica Clásica, Mir, Moscow, p. 76.
Brout, R., and Parentani, R. (1992)Nuclear Physics B,388, 474.
Brout, R., Parentani, R., and Spindel, P. (1991)Nuclear Physics B,353, 209.
Castagnino, M. A., Diener, R. B., Lara, L., and Puccini, G. (1997). Rigged Hilbert space and time asymmetry: The case of the upside-down harmonic oscillator,International Journal of Theoretical Physics, this issue.
Euler, H., and Kockel, B. (1935)Naturwissenschaften,23, 246.
Fanci, J. R. (1993).Parametrized Relativistic Quantum Theory, Kluwer, Boston.
Feshbach, H., and Villars, W. (1958)Reviews of Modern Physics,30, 24.
Feynman, R. P. (1948)Physical Review,74, 939.
Feynman, R. P. (1949a)Physical Review,76, 749.
Feynman, R. P. (1949b)Physical Review,76, 769.
Feynman, R. P. (1950)Physical Review,80, 440.
Feynman, R. P. (1951)Physical Review,84, 108.
Fock, V. (1973)Physikalische Zeitschrift Sowjetunion,12, 404.
Gaioli, F. H., and Garcia-Alvarez, E. T. (1994)General Relativity and Gravitation,26, 1267.
Garcia-Alvarez, E. T., and Gaioli, F. H. (1997). On the quantum electrodynamics of moving bodies,International Journal of Theoretical Physics, this issue.
Hartle, J. B., and Hawking, S. W. (1976)Physical Review D,13, 2188.
Heisenberg, W., and Euler, H. (1936)Zeitschrift für Physik,98, 714.
Horwitz, L. P., and Piron, C. (1973)Helvetica Physica Acta,46, 316.
Lifshitz, E. M., and Pitaevskii, L. P. (1971).Relativistic Quantum Theory, Part 2, Pergamon, Oxford, 1971, Section 126.
Nambu, Y. (1950)Progress of Theoretical Physics,5, 82.
Rumpf, H. (1977)Acta Physica Austriaca Supplementum 18, 873.
Rumpf, H., and Urbantke, H. K. (1978)Annals of Physics,114, 332.
Schwinger, J. (1951)Physical Review,82, 664.
Sonego, S. (1991)Physical Review A,44, 5369.
Stephens, C. R. (1988)Annals of Physics,181, 120.
Stueckelberg, E. C. G. (1941)Helvetica Physica Acta,14, 322.
Stueckelberg, E. C. G. (1942)Helvetica Physica Acta,15, 23.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gaioli, F.H., Garcia-Alvarez, E.T. & Castagnino, M.A. The Gamow vectors and the Schwinger effect. Int J Theor Phys 36, 2371–2389 (1997). https://doi.org/10.1007/BF02768930
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02768930