Class of very simple gauge theories which remain renormalizable even in the limit of infinite gauge coupling constant
A class of local gauge theories based on compact semisimple Lie groups is studied in the limit of infinite gauge coupling constant (g = infinity). In general, in this limit, the gauge fields become auxiliary in all gauge theories, and the system develops a richer structure of constraints. Unfortunately for most gauge theories, this limit turns out to be too singular to quantize and the theory ceases to be renormalizable. For a special class of gauge theories, however, where there are no fermions and there is only one multiplet of scalars in the adjoint representation, we prove that a consistent renormalizable quantum theory exists even in this very singular limit. We trace this exceptional behavior to a new local translationlike symmetry in the functional space that this class of gauge models possesses in the limit of infinite gauge coupling constant. By carrying out the constraint analysis, evaluating the Faddeev-Popov-Senjanovic determinant, and doing the functional integrations over the canonical momenta, the gauge fields, and most of the components of the scalar fields, we obtain an extremely simple result with no non-Abelian structure left in it. For example, for the group SU(2), the final answer reduces to the theory of a one-component self-interacting real phi/sup 4/ scalar field theory. Throughout this paper, we use functional methods and make no approximations; our results are nonperturbative and exact. We also discuss some of the possible implications of our results.
- Research Organization:
- Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794
- OSTI ID:
- 6082434
- Journal Information:
- Phys. Rev. D; (United States), Vol. 27:8
- Country of Publication:
- United States
- Language:
- English
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