Symmetries in noncommutative field theories: Hopf versus Lie

Vassilevich, D. V.

doi:10.11606/issn.2316-9028.v4i1p121-133

Cited by 6 publications

(7 citation statements)

References 43 publications

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“…[23]). This is in parallel to the observation made in [24] in the context of the Yang-Mills symmetries. By fixing a gauge in the gauge covariant star product one obtains a twisted-symmetric Yang-Mills theory [25].…”

Section: Noncommutative Gravity In Two Dimensionssupporting

confidence: 82%

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Diffeomorphism covariant star products and noncommutative gravity

Vassilevich¹

2009

Class. Quantum Grav.

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The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of all two-dimensional dilaton gravity models thus overcoming some difficulties of earlier approaches. One of such models appears to be integrable. We find all classical solutions of this model and discuss their properties.

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Section: Noncommutative Gravity In Two Dimensionssupporting

confidence: 82%

“…Next, let us substitute the fields (27) into eqs. (20) - (24). The equations still have the same form in terms of transformed the fields {Y u ,Ȳ u , e u µ ,ē u µ , Φ u }, except that ρ µ disappears.…”

Section: Noncommutative Gravity In Two Dimensionsmentioning

confidence: 96%

Diffeomorphism covariant star products and noncommutative gravity

Vassilevich¹

2009

Class. Quantum Grav.

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“…Twisting the diffeomorphism seems unnecessary, since we have these transformation realized in the standard way. Here we repeat the interpretation of twisted local symmetries suggested in [32,22]: twisted diffeomorphisms is what remains from the standard diffeomorphism symmetry when ω and ∇ are gauge fixed to some given values. It is also possible, that twisted symmetries are effective lowenergy symmetries when the noncommutativity is defined and fixed by some high-energy effects.…”

Section: Twist Representation Of the Star Productmentioning

confidence: 80%

Tensor calculus on noncommutative spaces

Vassilevich¹

2010

Class. Quantum Grav.

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It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an infinite number of degrees of freedom per point of the base manifold). We show that on a symplectic manifold this freedom may be almost completely eliminated if one extends the star product to all tensor fields in a covariant way and impose some natural conditions on the tensor algebra. The remaining ambiguity corresponds either to constant renormalizations to the symplectic structure, or to maps between classically equivalent field theory actions. We also discuss how one can introduce the Riemannian metric in this approach and the consequences of our results for noncommutative gravity theories.

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“…However, if one were to consider relaxing the concept of twisted symmetries and modify the definition of a deformed Leibniz rule (such as the one exhibited in (7.38)), several different twists and gauge invariants may be constructed that would lead to alternate formulations for NC gauge theories. Some new ideas in this context that might help to remove some of the inconsistencies pointed out here as well as elsewhere, are discussed in [34]. This would involve, essentially, assuming different deformations of products of elements in the same algebra of space-time functions A, when considering different transformation groups.…”

Section: Gauge Invariance Space-time Diffeomorphisms and Twistmentioning

confidence: 94%

Noncommutativity and Parametrization of Fields: The Scalar Electrodynamics Case

Juárez

Rosenbaum

Vergara

2010

Adv. Appl. Clifford Algebras

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The aim of this paper is to review the formalism of noncommutativity using canonical parametrization theory. In the first part we present the formalism for the case of Quantum Mechanics, and we show that using this approach and an appropriate basis we can get the noncommutativity expressed in terms of the Moyal product from the Dirac brackets of an extended phase space. We generalize our formalism to the context of Quantum Field Theory where we discuss the case of scalar electrodynamics. The interesting result is that our approach works correctly when we consider an interaction term between the gauge field and the scalar field. Finally, we present an argument that shows that gauge theories are not deformed if we use only noncommutativity of the coordinates. Mathematics Subject Classification (2000). Primary 70S10, 70S05; Secondary 81T75, 20C20.

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Symmetries in noncommutative field theories: Hopf versus Lie

Cited by 6 publications

References 43 publications

Diffeomorphism covariant star products and noncommutative gravity

Diffeomorphism covariant star products and noncommutative gravity

Tensor calculus on noncommutative spaces

Noncommutativity and Parametrization of Fields: The Scalar Electrodynamics Case

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