2005
DOI: 10.1088/1742-6596/24/1/023
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Non-commutativity in gravity, topological gravity and cosmology

Abstract: Abstract. In this work we present different results obtained, in analyzing several aspects of gravity in non commutative space-time. We obtain generalized Euler and Pontrgajin topological invariants, and argue the possibility of defining new topological invariants in the same manner. Also a non commutative self dual gravity is constructed. Finally a proposal of non commutative quantum cosmology is also given.

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Cited by 9 publications
(7 citation statements)
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“…Moreover, we find in the literature that the topological theories are also important in the canonical approach of GR; In fact, when GR is considered with the addition of topological terms, namely the Pontryagin, Euler and Nieh Yan invariants, it is well-known that these topological invariants have no effect on the equations of motion of gravity, however, they give an important contribution in the symplectic structure of the theory [5]. Within the classical field theory context, either the Euler or Pontryagin classes are fundamental blocks for constructing the noncommutative form of topolog-ical gravity [6]. Furthermore, these topological invariants have been studied in several works due to they are expected to be related to physical observables, as for instance, in the case of anomalies [7][8][9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Moreover, we find in the literature that the topological theories are also important in the canonical approach of GR; In fact, when GR is considered with the addition of topological terms, namely the Pontryagin, Euler and Nieh Yan invariants, it is well-known that these topological invariants have no effect on the equations of motion of gravity, however, they give an important contribution in the symplectic structure of the theory [5]. Within the classical field theory context, either the Euler or Pontryagin classes are fundamental blocks for constructing the noncommutative form of topolog-ical gravity [6]. Furthermore, these topological invariants have been studied in several works due to they are expected to be related to physical observables, as for instance, in the case of anomalies [7][8][9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%
“…ical gravity [6]. Furthermore, these topological invariants have been studied in several works due to they are expected to be related to physical observables, as for instance, in the case of anomalies [7][8][9][10][11][12].…”
mentioning
confidence: 99%
“…However, it has provoked controversy about whether or not the Nieh-Yan term contributes to the chiral anomaly in 4D spacetime with torsion [8,9]. Pontryagin and Euler forms were also shown to be crucial for non-commutative topological gravity [10]. In addition, a symplectic analysis of both curvature-based topological invariants [11] showed that they are different in structure after a quantization process.…”
Section: Introductionmentioning
confidence: 99%
“…However, it has provoked controversy about whether or not the Nieh-Yan term contributes to the chiral anomaly in a 4D spacetime with torsion [6]. Pontryagin and Euler forms were also shown to be crucial for non-commutative topological gravity [7]. Besides, symplectic analysis of both curvature-based topological invariants [8] showed that they are different in structure after a quantization process.…”
Section: Introductionmentioning
confidence: 99%