Twist as a symmetry principle and the noncommutative gauge theory formulation

Chaichian, M.; Tureanu, Anca; Zet, G.

doi:10.1016/j.physletb.2007.06.026

Cited by 28 publications

(47 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, there is no restriction on the allowed gauge groups for which the twist deformation can be implemented [5,48]. This is radically different from the usual definition in noncommutative gauge theory [25,44], and has also been a focal point of much debate in the literature [2,17,18].…”

Section: Wilson Loop Operatorsmentioning

confidence: 99%

Wilson loops and area-preserving diffeomorphisms in twisted noncommutative gauge theory

Riccardi

Szabo

2007

Phys. Rev. D

View full text Add to dashboard Cite

We use twist deformation techniques to analyse the behaviour under area-preserving diffeomorphisms of quantum averages of Wilson loops in Yang-Mills theory on the noncommutative plane. We find that while the classical gauge theory is manifestly twist covariant, the holonomy operators break the quantum implementation of the twisted symmetry in the usual formal definition of the twisted quantum field theory. These results are deduced by analysing general criteria which guarantee twist invariance of noncommutative quantum field theories. From this a number of general results are also obtained, such as the twisted symplectic invariance of noncommutative scalar quantum field theories with polynomial interactions and the existence of a large class of holonomy operators with both twisted gauge covariance and twisted symplectic invariance.

show abstract

Section: Wilson Loop Operatorsmentioning

confidence: 99%

Wilson loops and area-preserving diffeomorphisms in twisted noncommutative gauge theory

Riccardi

Szabo

2007

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…The map (27), regarding (31), converts the noncommutative Hamiltonian (30) into a new commutative one…”

Section: Signature Change In Noncommutative Phase Spacementioning

confidence: 99%

Signature Change in Noncommutative FRW Cosmology

2012

View full text Add to dashboard Cite

The conditions for which the no boundary proposal may have a classical realization of a continuous change of signature, are investigated for a cosmological model described by FRW metric coupled with a self interacting scalar field, having a noncommutative phase space of dynamical variables. The model is then quantized and a good correspondence is shown between the classical and quantum cosmology indicating that the noncommutativity does not destruct the classical-quantum correspondence. It is also shown that the quantum cosmology supports a signature transition where the bare cosmological constant takes a vast continuous spectrum of negative values. The bounds of bare cosmological constant are limited by the values of noncommutative parameters. Moreover, it turns out that the physical parameters are constrained by the noncommutativity parametres.

show abstract

“…For this purpose let us first begin by deriving the Poisson bracket of the projection A a of the 4-vector potential field A α on the hypersurface Σ with * H τ [ξ]. Making use of (3.4) and (3.6) we get 12) after also making use of the expression…”

Section: Parametrized Maxwell F Ield and Canonical Representation Of mentioning

confidence: 99%

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Rosenbaum¹

2008

SIGMA

View full text Add to dashboard Cite

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.

show abstract

Twist as a symmetry principle and the noncommutative gauge theory formulation

Cited by 28 publications

References 18 publications

Wilson loops and area-preserving diffeomorphisms in twisted noncommutative gauge theory

Wilson loops and area-preserving diffeomorphisms in twisted noncommutative gauge theory

Signature Change in Noncommutative FRW Cosmology

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Contact Info

Product

Resources

About