Exact Renormalization Group for Gauge Theories
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe — quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored.
KeywordsGauge Theory Gauge Transformation Effective Action Gauge Field Background Field
Unable to display preview. Download preview PDF.
- 5.D. Brydges, J. Fröhlich, E. Seiler, On the construction of quantized gauge fields. I. General results, Ann. Phys. 121:227 (1979), II. Convergence of the lattice approximation, Commun. Math. Phys. 71:159 (1980), III. The twodimensional abelian Higgs model without cutoffs, Commun. Math. Phys. 79:353 (1981).ADSCrossRefGoogle Scholar
- 8.E. Seiler, “Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics,” Lecture Notes in Physics, vol. 159, Springer-Verlag, Berlin-Heidelberg-New York (1982).Google Scholar
- 9.T. Balaban, (Higgs)2,3 quantum fields in a finite volume. I. A lower bound, Commun. Math. Phys. 85:603 (1983). II. An upper bound, Commun. Math. Phys. 86:555 (1982). III. Renormalization, Commun. Math. Phys. 88:411 (1983). Regularity and decay of lattice Green’s functions, 89:571 (1983).MathSciNetADSCrossRefGoogle Scholar
- 10.T. Balaban, Propagators and renormalization transformations for lattice gauge theories, I., Harvard University preprint HUTMP-B139.Google Scholar
- 11.T. Balaban, Renormalization group approach to nonabelian gauge field theories, in: “Mathematical Problems in Theoretical Physics, Proceedings of the VII-th International Conference on Mathematical Physics, Boulder, 1983,” Lecture Notes in Physics, Springer-Verlag, Berlin-Heidelberg-New York, to appear.Google Scholar
- 12.T. Balaban, D. Brydges, J. Imbrie, A. Jaffe, The mass gap the Higgs models on a unit lattice. Harvard University preprint.Google Scholar