Effective Lagrangians and current algebra in three dimensions
In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnetics (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co-homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non-perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorm and compute the critical exponents in a specific limiting case, the CP{sup N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.
- Research Organization:
- Rochester Univ., NY (United States)
- OSTI ID:
- 121346
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 1993
- Country of Publication:
- United States
- Language:
- English
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