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Dynamical Effects of the Chern-Simons Term


2+1 dimensional quantum field theories have aroused a great deal of interest in the recent years. Such theories are good theoretical laboratories because they simulate many 3+1 dimensional properties ín a simpler setting. Besides, their peculiar structure motivares applications to the condensed matter physics. This research project focuses the study of methods and applications of 2+1 dímensionalquantum field theory. As a matter of convenience, to simplify the presentation, the plan has been separated into three parts which, of course, are not disjointed. The first part is concentrated into problems concerning the non relativistic limit of field theories, establishing connections with the Aharonov-Bohm scattering and also motivating possible applications to condensed matter physics (Quantum Hall effect and high temperature superconductivity). In the next part of the plan, we relate some quantization/renormalization problems of Chern-Simons theories. In particular, as an alternative to the use of dimensional regularization, we intend to investigate applications of extended BPHZ schemes (the so called soft schemes, in which mass parameters participate in the subtractions and have a smooth asymptotie behavior) to models with (spontaneously) broken symmetries. We also propose to study four fermion nonrenormalizable models (with Thirring and/or Gross-Neveu likes elf-ínteractions) as effective field theories for low energy physies. Renormalization group methods will be applied to the present situation and the critical structure of various models with the Chern-Simons term wili be studied. In the large N limit non perturbative effects will be investigated with particular concern on the existence of double scaling limits. The last part of the plan refers to temperature effects. One interesting problem in this class is the understanding of the behavior of the coefficient of the Chern-Simons term. Ask nown, in the nonabelian situation and even in the Abelian case but with a nontrivial topology gauge invariance implies in the quantization of this coefficient, only certain values being admissible. However, this property and therefore gauge invariance seems to be lost as the temperature is turned on. Since the beginning of this decade, 2+1 dimensional field theory investigations have been developed by the proponents of this plan. The results so far obtained concern the spontaneous breaking of parity, infrared structure of QED3, bound states and nonrelativistic limit. This experience wili be helpful to accomplish the plan. (AU)

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