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Geometric quantization, Chern-Simons quantum mechanics and one-dimensional sigma models
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In this article, the classical theory of a topological model which is constructed by setting the kinetic term of a (one-dimensional) sigma model at the classical level equal to zero is examined.Abstract:
The classical theory of a topological model which is constructed by setting the kinetic term of a (one-dimensional) sigma model at the classical level equal to zero is examined. The constraints and the geometry of the phase space of the supersymmetric extensions of the topological theory are studied. The rigid symmetries of a (supersymmetric) sigma model and its corresponding topological theory are gauged. Finally, the author examines the quantum theory of the one-dimensional sigma model in the limit where its kinetic term is set equal to zero and compare it with the quantum theory of the corresponding topological model.read more
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Gauged Wess-Zumino terms and equivariant cohomology
TL;DR: In this article, the problem of measuring the Wess-Zumino term of a d-dimensional bosonic σ-model has been studied and it has been shown that the obstructions to gauging a WZ term can be understood in terms of the equivariant cohomology of the target space and this allows us to use topological tools to derive vanishing theorems guaranteeing the absence of obstructions for a large class of target spaces and symmetry groups in the physically interesting dimensions d≤4.
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Supersymmetric sigma models, gauge theories and vortices
TL;DR: In this article, the scalar potential for a large class of supersymmetric nonlinear sigma models with Wess-Zumino terms was derived, and the Euclidean actions of the (2,0) and (4,0)-supersymmetric models were shown to be bounded by topological charges, which involved the equivariant extensions of the Kahler forms of the sigma model target spaces.
Journal ArticleDOI
The canonical structure of Wess-Zumino-Witten models
G. Papadopoulos,B. Spence +1 more
TL;DR: In this article, the phase space of the Wess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group G is defined and the corresponding symplectic form is given.
Journal ArticleDOI
Deformation quantization of a dimensionally reduced Seiberg-Witten moduli space
TL;DR: In this article, it was shown that the moduli space N of the dimensionally reduced Seiberg-Witten equations with a Higgs field has a symplectic form Ω.
References
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Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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Quantised Singularities in the Electromagnetic Field
TL;DR: The steady progress of physics requires for its theoretical formulation a mathematics that gets continually more advanced as discussed by the authors, and it seems likely that this process of increasing abstraction will continue in the future and that advance in physics is to be associated with a continual modification and generalisation of the axioms at the base of the mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
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A mass term for three-dimensional gauge fields
TL;DR: In this article, a mass term for gauge fields in three-dimensional spacetime was proposed, where the Aμ is a Lie algebra representation of the Poincare algebra with only one polarization for spin equal to any real number, integral multiple of one-half or otherwise.