Abstract
Lattice gauge theories may be looked at as perturbations of the theory of a vector field with a Gaussian action. We study this theory here and in following papers obtaining crucial results for understanding the renormalization group method in more complicated non-Abelian gauge field theories.
Similar content being viewed by others
References
Balaban, T.: (Higgs)2,3 quantum fields in a finite volume. I. A lower bound. Commun. Math. Phys.85, 603–636 (1982), and references therein
Balaban, T.: Regularity and decay of lattice Green's functions. Commun. Math. Phys.89, 571–597 (1983)
Balaban, T.: Renormalization group methods in non-Abelian gauge theories. Harvard preprint HUTMP B134
Brydges, D. C., Federbush, P.: A lower bound for the mass of a random Gaussian lattice. Commun. Math. Phys.62, 79–82 (1978)
Brydges, D. C., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. I. General results. Ann. Phys.121, 227–284 (1979)
Brydges, D. C., Fröhlich, J., Seiler, E.: Construction of quantised gauge fields. II. Convergence of the lattice approximation. Commun. Math. Phys.71, 159–205 (1980).
Wilson, K. G., Bell, T. L.: Finite-lattice approximations to renormalization groups. Phys. Rev.B11, 3431–3445 (1975)
Wilson, K. G.: Quantum chromodynamics on a lattice. In: Quantum Field Theory and Statistical Mechanics, Cargèse 1976, M. Levy and P. Mitter (eds.). New York: Plenom Press, 1977, pp. 143–172
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Research supported in part by the National Science Foundation under Grant PHY-82-03669
Rights and permissions
About this article
Cite this article
Balaban, T. Propagators and renormalization transformations for lattice gauge theories. I. Commun.Math. Phys. 95, 17–40 (1984). https://doi.org/10.1007/BF01215753
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01215753