Deformed Gauge Theories

Wess, Julius

doi:10.1007/978-3-540-89793-4_2

Cited by 6 publications

(15 citation statements)

References 18 publications

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“…Equations (5.18) and (5.19) agree with those on which [11] is based when remarking on some of the conclusions on deformed gauge theories arrived at in [10,9,30,31]. Indeed, one basic idea in this other approach of gauge twisted theories is the assumption that the gauge generators δᾱ :=ᾱ(X) =ᾱ B (X)T B act on particle and gauge fields with the usual point product, so instead of (5.17) they define…”

Section: Noncommutative Gauge Theoriessupporting

confidence: 67%

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Rosenbaum¹

2008

SIGMA

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Abstract. In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382] we have shown how for canonical parametrized field theories, where spacetime is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchař K.V., Ann. Physics 164 (1985), [316][317][318][319][320][321][322][323][324][325][326][327][328][329][330][331][332][333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchař and Stone for the case of the parametrized Maxwell field in [Kuchař K.V., Stone S.L., Classical Quantum Gravity 4 (1987), [319][320][321][322][323][324][325][326][327][328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

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Section: Noncommutative Gauge Theoriessupporting

confidence: 67%

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Rosenbaum¹

2008

SIGMA

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“…In the process we prove that the functional derivative methods introduced in Ref. [34] for gauge fields, can be carried over to the construction of noncommutative gravitational fields with twisted symmetries (a basic detailed calculation is summarized in the appendix). In Section III we give an overview of self-dual gravity.…”

Section: Introductionmentioning

confidence: 94%

“…In [34], J. Wess has given an explicit realization of the twisted co-product (1) for gauge symmetry. This formulation makes use of the functional calculus language from field theory, which allows to explicitly restrict the transformations to the fields, and to avoid the problem that the derivatives of the Moyal product are not covariant.…”

Section: Introductionmentioning

confidence: 99%

Twisted covariant noncommutative self-dual gravity

et al. 2008

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A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the θ-expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in θ for the Plebański action is explicitly obtained.

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“…The approach to the so-called "twisted gauge theories" which we present in this subsection goes back to J. Wess and his group 27 . For a recent review, see [203,204,205] and references therein. The main idea is, in addition to the pointwise product, to also deform the Leibniz rule by using Hopf algebra techniques.…”

Section: Twisted Gauge Theoriesmentioning

confidence: 99%

Gauge Theories on Deformed Spaces

Blaschke

Kronberger

Sedmik³

et al. 2010

SIGMA

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Abstract. The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.

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Deformed Gauge Theories

Cited by 6 publications

References 18 publications

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Twisted covariant noncommutative self-dual gravity

Gauge Theories on Deformed Spaces

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