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

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, alt...

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Published in:arXiv.org
Main Authors: Aldaya, V, Calixto, M, Guerrero, J, López-Ruiz, F F
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 16.12.2010
Subjects:
Equivalence principle
Field theory
Linear systems
Measurement
Nonlinear systems
Particle interactions
Quantum field theory
Quantum theory
Symmetry
ISSN:2331-8422
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Abstract 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.
AbstractList 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.
Author Aldaya, V
López-Ruiz, F F
Guerrero, J
Calixto, M
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SubjectTerms Equivalence principle
Field theory
Linear systems
Measurement
Nonlinear systems
Particle interactions
Quantum field theory
Quantum theory
Symmetry
Title Symmetries of Non-Linear Systems: Group Approach to their Quantization
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