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Quantization of a gauge theory with independent metric and connection fields
Phys. Rev. D 34, 3012 – Published 15 November, 1986
DOI: https://doi.org/10.1103/PhysRevD.34.3012
Abstract
We carry out the Hamiltonian quantization of a member of a class of gauge theories in which the internal metric becomes an independent degree of freedom and the gauge group is generalized to SL(N,C). The Hamiltonian quantization is carried out both in a gauge where only the SU(N) symmetry is manifest and in a gauge-invariant way. These theories have been proposed by Cahill, and they also arise as the nongravitational sector of a unified theory of gravitational and gauge fields which has been proposed by one of us (J.D.). The physical degrees of freedom are identified and a relativistically invariant functional generator is constructed. The resulting quantum theory is stable, but not perturbatively renormalizable.
References (12)
- The internal sector of this theory was first proposed by K. Cahill, Phys. Rev. D 18, 2930 (1978); ibid. 20, 2636 (1979); J. Math. Phys. 21, 2676 (1980) Phys. Rev. D 26, 1916 (1982) see also J. E. Kim and A. Zee, ibid. 21, 1939 (1980); B. Julia and F. Luciani, Phys. Lett. 90B, 270 (1980).
- J. Dell, University of Maryland report, 1979 (unpublished); Ph.D. dissertation, University of Maryland, 1981; University of Texas report, 1983 (unpublished).
- D. E. Neville, Phys. Rev. D 21, 865 (1980); ibid. 21, 2075 (1980); ibid. 21, 2770 (1980); ibid. 23, 1244 (1981); E. Sezgin and P. van Nieuwenhuizen, ibid 21, 3269 (1980).
- L. Smolin, Nucl. Phys. B160, 253 (1979).
- See for example, the article by D. Boulware, A. Strominger, and E. Tomboulis, in Quantum Theory of Gravity, Essays in Honor of the 60th birthday of Bryce DeWitt, edited by S. Christensen (Hilger, Bristol, 1984), and references therein.
- Lee Smolin, Nucl. Phys. B247, 511 (1984).
- P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University Press, New York, 1964).
- A. Hanson, T. Regge, and C. Teitelboim, Constrained Hamiltonian Systems (Academia Nazionale Dei Lincei, Rome, 1976).
- D. S. Popovic, Phys. Rev. D 34, 1764 (1986).
- P. Senjanovic, Ann. Phys. (N.Y.) 100, 227 (1976). The form of the path integral for systems with second-class constraints is also given in E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975).
- L. D. Faddeev and A. A. Slavnov, Gauge Fields: Introduction to the Quantum Theory (Benjamin, New York, 1980); C. Itzykson and J. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
- Lee Smolin, Phys. Rev. D 30, 2159 (1984).