Twisted covariant noncommutative self-dual gravity

Estrada-Jiménez, Sendic; García‐Compeán, Hugo; Obregón, O.; Ramı́rez, C.

doi:10.1103/physrevd.78.124008

Cited by 28 publications

(31 citation statements)

References 63 publications

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“…Several proposals for such an effective theory have been made [3,4] in the recent past, including the so-called twistdeformed diffeomorphism models [5,6]. Even though these models preserve what are called twisted diffeomorphisms, they violate invariance under conventional diffeomorphisms [7].…”

Section: Introductionmentioning

confidence: 97%

Seiberg-Witten maps forSO(1,3)gauge invariance and deformations of gravity

Mǎrculescu

Ruiz

2009

Phys. Rev. D

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A family of diffeomorphism-invariant Seiberg-Witten deformations of gravity is constructed. In a first step Seiberg-Witten maps for an SOð1; 3Þ gauge symmetry are obtained for constant deformation parameters. This includes maps for the vierbein, the spin connection, and the Einstein-Hilbert Lagrangian. In a second step the vierbein postulate is imposed in normal coordinates and the deformation parameters are identified with the components ðxÞ of a covariantly constant bivector. This procedure gives for the classical action a power series in the bivector components which by construction is diffeomorphism invariant. Explicit contributions up to second order are obtained. For completeness a cosmological constant term is included in the analysis. Covariant constancy of ðxÞ, together with the field equations, imply that, up to second order, only four-dimensional metrics which are direct sums of two two-dimensional metrics are admissible, the two-dimensional curvatures being expressed in terms of . These four-dimensional metrics can be viewed as a family of deformed emergent gravities.

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Section: Introductionmentioning

confidence: 97%

Seiberg-Witten maps forSO(1,3)gauge invariance and deformations of gravity

Mǎrculescu

Ruiz

2009

Phys. Rev. D

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“…We find it encouraging that the self-dual option can be pursued to the extent shown in our paper, without any use of the Seiberg-Witten map or yet other techniques applied in the previous literature [24][25][26][27][28][29][30][31][32][33][34][35][36][37] Appendix A: Twist differential geometry…”

Section: Results and Open Problemsmentioning

confidence: 73%

Self-dual road to noncommutative gravity with twist: A new analysis

2014

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The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form should vanish, and that the Lorentz-Lie-algebravalued part of the full connection 1-form should be self-dual. Other two conditions, expressing self-duality of a pair 2-forms occurring in the full curvature 2-form, are also imposed. This leads to a systematic solution strategy, here displayed for the first time, where all parts of the connection 1-form are first evaluated, hence the full curvature 2-form, and eventually all parts of the tetrad 1-form, when expanded on the basis of γ-matrices. By assuming asymptotic expansions which hold up to first order in the noncommutativity matrix in the neighbourhood of the vanishing value for noncommutativity, we find a family of self-dual solutions of the field equations. This is generated by solving first a inhomogeneous wave equation on 1-forms in a classical curved spacetime (which is itself self-dual and solves the vacuum Einstein equations), subject to the Lorenz gauge condition.In particular, when the classical undeformed geometry is Kasner spacetime, the above scheme is fully computable out of solutions of the scalar wave equation in such a Kasner model.

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“…To resume, the quantization given in [1] and as used in more recent investigations [5,6] are very similar to ours. However, there are differences.…”

Section: Comparison To H S Snyder's Workmentioning

confidence: 58%

“…It may be a matrix with constant entries, as used in the Moyal product [5,6], or it may be more general, being a function on operators, as used in [1].…”

Section: Consequences Of the Quantization Rules Listed In Eq (33)mentioning

confidence: 99%

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A proposal of quantization in flat space‐time with a minimal length present

Hess

2015

Astron Nachr

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Abstract. The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with noncommuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4-dimensional sub-space. The similarities to H. S. Snyder's work, a former proposal to include the effects of a minimal length, are exposed. The first steps to pseudo-complex Quantum Mechanics in 1-dimension are outlined, awaiting still the interpretation of some new emerging structures. As an example, two waves, out of phase by 90 degrees, are added which classically annihilate each other, while in the pseudo-complex description there is a non-zero amplitude.

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Twisted covariant noncommutative self-dual gravity

Cited by 28 publications

References 63 publications

Seiberg-Witten maps forSO(1,3)gauge invariance and deformations of gravity

Seiberg-Witten maps forSO(1,3)gauge invariance and deformations of gravity

Self-dual road to noncommutative gravity with twist: A new analysis

A proposal of quantization in flat space‐time with a minimal length present

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