Symmetries of Non-Linear Systems: Group Approach to their Quantization

Details Symmetries of Non-Linear Systems: Group Approach to their Quantization Symmetries of Non-Linear Systems: Group Approach to their Quantization

2010-12-16

arxiv.org/abs/1012.3681v1

International Journal of Geometric Methods in Modern Physics 8 (2011) 1329-1354

Physics

Mathematical Physics

24 pages, LaTeX, no figures

Scientific paper

10.1142/S0219887811005713

We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically non-perturbative, is primarily intended for non-linear systems, although needless to say that finding the basic symmetry associated with a given (quantum) physical problem is in general a difficult task, which many times nearly emulates the complexity of finding the actual (classical) solutions. Apart from some interesting examples related to the electromagnetic and gravitational particle interactions, where an algebraic version of the equivalence principle naturally arises, we attempt to the quantum description of non-linear sigma models. In particular, we present the actual quantization of the partial-trace non-linear SU(2) sigma model as a representative case of non-linear quantum field theory.

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