Twist symmetry and gauge invariance

Chaichian, M.; Tureanu, Anca

doi:10.1016/j.physletb.2006.04.040

Cited by 47 publications

(54 citation statements)

References 16 publications

(27 reference statements)

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“…Another essential peculiarity of NCQFT consists in the well-known fact that not every gauge group is closed with respect to the star-gauge transformations which underlie the standard approach to NC gauge theories. Recently it was proposed an idea that not only Poincare but also internal symmetry can be twisted [35], [36] (see also [37] for alternative point of view). In this approach the transformation law of primary fields is left undeformed while the comultiplication is twisted leading to the deformation of the Leibniz rule.…”

Section: Remarks On Twisted Gauge Symmetriesmentioning

confidence: 99%

Heat Kernel of Nonminimal Gauge Field Kinetic Operators on Moyal Plane

Strelchenko

2007

Int. J. Mod. Phys. A

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We generalize the Endo formula [1] originally developed for the computation of the heat kernel asymptotic expansion for non-minimal operators in commutative gauge theories to the noncommutative case. In this way, the first three non-zero heat trace coefficients of the non-minimal U (N ) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U (1) sector of the gauge model. The non-planar or mixed heat kernel coefficients are shown to be gaugefixing dependent in any dimension of space-time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce non-local gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U (N ) model at one-loop level. Such phenomenon was observed at first in Ref.[2] for space-like noncommutative φ 4 scalar and U (1) gauge theories. The twisted-gauge transformation approach is discussed.

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Section: Remarks On Twisted Gauge Symmetriesmentioning

confidence: 99%

Heat Kernel of Nonminimal Gauge Field Kinetic Operators on Moyal Plane

Strelchenko

2007

Int. J. Mod. Phys. A

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“…However, to have a similar action on the star product of two elements f, g the parameters α j have to be noncommutative (see (25)). …”

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confidence: 99%

“…Application of the abelian twist to gauge field theories are also considered (see [25] and references therein).…”

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confidence: 99%

Twists of quantum groups and noncommutative field theory

Kulish

2007

J Math Sci

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The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups, the noncommutative (super)space-time defined by coordinates with Heisenberg commutation relations, is (super)Poincaré invariant, as well as the corresponding field theory. Noncommutative parameters of global transformations are introduced.

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“…Moreover, by assuming that the algebra of the gauge generators can be given an additional Hopf bialgebra structure, and that the derivatives of any order of the gauge and particle fields are, as noted in [11], in the same representation of the gauge algebra as the fields themselves, one could further write…”

Section: Noncommutative Gauge Theoriesmentioning

confidence: 99%

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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Twist symmetry and gauge invariance

Cited by 47 publications

References 16 publications

Heat Kernel of Nonminimal Gauge Field Kinetic Operators on Moyal Plane

Heat Kernel of Nonminimal Gauge Field Kinetic Operators on Moyal Plane

Twists of quantum groups and noncommutative field theory

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

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