Abstract
A Lagrangian in (1 + 3)-dimensional space-time which describes the interaction of photons, electrons, and phonons is proposed. This is a generalization of Rodriguez-Nuñez' model. This Lagrangian is also singular in the sense of Dirac. The path-integral quantization of this system is performed with the aid of the Dirac formalism for a singular Lagrangian and the method of functional integration. The phase-space generating functional of the Green function of this system is deduced. The Ward identities in canonical formalism for local symmetries are derived, and the Ward identities of proper vertices for this system are obtained. The conserved charges at the quantum level are also obtained. The effective Lagrangian in configuration space for the present model is derived in the case ρ = const. Thus, the Feynman rule can be deduced immediately.
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References
Banerjee, R. (1993).Physical Review D,48, 2905.
Banerjee, R. (1994).Nuclear Physics B,419, 611.
Danilov, G. S. (1991).Physics Letters B,257, 285.
Dirac, P. A. M. (1964).Lectures in Quantum Mechanics, Yeshiva University, New York.
Du, T.-S., Yin, H.-C., and Ruan, T.-N. (1980).Nuclear Physics B,164, 103.
Faddeev, L. D. (1970).Theoretical Mathematics and Physics,1, 1.
Gerstein, I. S., Jackiw, R., Lee, B. W., and Weinberg, S. (1971).Physical Review D,3, 2468.
Haken, H. (1976).Quantum Field Theory of Solids, North-Holland, Amsterdam.
Joglekar, S. D. (1991).Physical Review D,44, 3879.
Kim, J. K., Kim, W.-T., and Shin, H. (1994).Journal of Physics A: Mathematical and General,27, 6067.
Lee, T. D., and Yang, C. N. (1962).Physical Review,128, 885.
Lhallabi, T. (1989).International Journal of Theoretical Physics,28, 875.
Li, Z.-P. (1987).International Journal of Theoretical Physics,26, 853.
Li, Z.-P. (1991).Journal of Physics A: Mathematical and General,24, 4261.
Li, Z.-P. (1993). Classical and quantal dynamics of the constrained system and their symmetry properties, Beijing Polytechnic University.
Li, Z.-P. (1995).International Journal of Theoretical Physics,34, 523.
Mizrahi, M. M. (1978).Journal of Mathematical Physics,19, 298.
Nash, C. (1978).Relativistic Quantum Fields, Academic Press, New York.
Rodriguez-Nuñez, J. J. (1990).International Journal of Theoretical Physics,29, 467.
Schweber, S. S. (1961).An Introduction to Relativistic Quantum Field Theory, Harper and Row, New York.
Senjanovic, P. (1976).Annals of Physics,100, 227.
Slavnov, A. A. (1972).Theoretical and Mathematical Physics,10, 99.
Suura, H., and Young, B.-L. (1973).Physical Review D,8, 4353.
Takahashi, Y. (1957).Nuovo Cimento,6, 370.
Taylor, J. C. (1972).Nuclear Physics B,33, 436.
Ward, J. C. (1950).Physical Review,77, 2931.
Young, B.-L. (1987).Introduction to Quantum Field Theories, Science Press, Beijing.
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Li, Zp. Quantum field theory for a system of interacting photons, electrons, and phonons. Int J Theor Phys 35, 1353–1368 (1996). https://doi.org/10.1007/BF02084945
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DOI: https://doi.org/10.1007/BF02084945