Consistent construction of perturbation theoryon non-commutative spaces

Denk, Stefan; Putz, Volkmar; Wohlgenannt, Michael

doi:10.1140/epjc/s2005-02410-y

Cited by 3 publications

(4 citation statements)

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“…We have presented a careful discussion of electroweak charged and neutral currents as well as a derivation of the Higgs and Yukawa terms of the NCSM action. Among the novel features in comparison with previous works [6,9] are the appearance of additional gauge boson interaction terms (30) and (61) CP violation induced by space-time non-commutativity has potential to be a particular sensitive probe of non-commutativity [33]. The analysis of C,P,T properties of the NCSM and the NCGUTs [31] shows that θ transforms under C, P, T in such a way that it preserves these discrete symmetries in the action.…”

Section: Discussionmentioning

confidence: 89%

“…These problems can be overcome by a careful analysis of perturbation theory in a Hamiltonian approach, cf. [20,30] for scalar field theory. Other problems in non-commutative theories that are encountered already at the classical level are charge quantization in noncommutative QED, the definition of the tensor product of gauge fields, gauge invariance of the Yukawa couplings and ambiguities in the kinetic part of the action for gauge fields.…”

Section: Non-commutative Standard Modelmentioning

confidence: 99%

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The standard model on non-commutative space-time: electroweak currents and the Higgs sector

et al. 2005

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Section: Discussionmentioning

confidence: 89%

Section: Non-commutative Standard Modelmentioning

confidence: 99%

The standard model on non-commutative space-time: electroweak currents and the Higgs sector

et al. 2005

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“…Since in the special case of d = D/2 = 2 only two pairs of creation and annihilation operators arise, they are denoted with a m ,a † m and b m , b † m instead of distinguishing them by an index. The components of the tetrad field operator êµ m can be expressed by the operators (17) as follows:…”

Section: Definition Of Coherent States Concerning the Gravitational F...mentioning

confidence: 99%

Canonical noncommutativity algebra for the tetrad field in general relativity

Kober

2011

Class. Quantum Grav.

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General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the noncommutativity algebra of the coordinates in the canonical case of noncommutative geometry, this idea is closely related to noncommutative geometry as well as to canonical quantization of gravity. According to this presupposition generalized field equations for general relativity are derived which are obtained by replacing the usual tetrad field by the tetrad field operator within the actions and then building expectation values of the corresponding field equations between coherent states. These coherent states refer to creation and annihilation operators created from the components of the tetrad field operator. In this sense the obtained theory could be regarded as a kind of semiclassical approximation of a complete quantum description of gravity. The consideration presupposes a special choice of the tensor determining the algebra providing a division of space-time into two two-dimensional planes.

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“…This has been done for a noncommutative scalar field theory in [18,19,20] and for noncommutative QED in [21,22]. For some other attempts, see [23,24,25]. Reducing the nonlocality of the noncommutative field theories to a finite range is also an option which has been preliminarily exploited in [26,27].…”

Section: Conclusion and Remarksmentioning

confidence: 99%