Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

Ohl, Thorsten; Schenkel, Alexander

doi:10.1007/s10714-010-1016-2

Cited by 10 publications

(33 citation statements)

References 39 publications

(85 reference statements)

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“…functions) 1 . A different study of a Klein-Gordon action in a curved background is presented in [5,6], based on the metric formulation of twist noncommutative gravity [7], where noncommutative local Lorentz symmetry is absent.…”

Section: Introductionmentioning

confidence: 99%

Extended gravity theories from dynamical noncommutativity

Aschieri

Castellani

2012

Gen Relativ Gravit

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In this paper we couple noncommutative (NC) vielbein gravity to scalar fields. Noncommutativity is encoded in a ⋆-product between forms, given by an abelian twist (a twist with commuting vector fields). A geometric generalization of the SeibergWitten map for abelian twists yields an extended theory of gravity coupled to scalars, where all fields are ordinary (commutative) fields. The vectors defining the twist can be related to the scalar fields and their derivatives, and hence acquire dynamics. Higher derivative corrections to the classical Einstein-Hilbert and Klein-Gordon actions are organized in successive powers of the noncommutativity parameter θ AB .

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Section: Introductionmentioning

confidence: 99%

Extended gravity theories from dynamical noncommutativity

Aschieri

Castellani

2012

Gen Relativ Gravit

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“…See his recent review [28] and references therein. Also, there are many closely related works [29][30][31][32][33][34][35][36][37]. However, the emergent gravity based on noncommutative field theories is relatively new, so it would be premature to have an extensive review about this subject because it is still in an early stage of development.…”

Section: Outline Of the Papermentioning

confidence: 99%

Quantum gravity from noncommutative spacetime

Lee

Yang

2014

Journal of the Korean Physical Society

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We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U (1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U (1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ⋆-algebra) of quantum gravity.

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“…Our work is based on the approach initiated by Julius Wess and his group [2,3], in which a particular emphasis is given to the deformed Hopf algebra of diffeomorphisms. For exact solutions of the noncommutative Einstein equations see [4,5,6] and for quantum field theory on noncommutative curved spacetimes based on this formalism see [7,8,9,10]. Other recent mathematical developments in noncommutative (and also nonassociative) differential geometry and Riemannian geometry can be found in the papers of Beggs and Majid [11,12].…”

Section: Introductionmentioning

confidence: 99%

Twist deformations of module homomorphisms and connections

Schenkel¹

2012

Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011)

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Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the right A -linear endomorphisms of V , with A ,V denoting the usual twist deformations of A,V . The quantization map is extended to right A-linear homomorphisms between left H-module A-bimodules and to right connections on V . We then investigate the tensor product of linear maps between left H-modules. Given a quasitriangular Hopf algebra we can define an H-covariant tensor product of linear maps, which restricts for left H-module A-bimodules to a well-defined tensor product of right A-linear homomorphisms on tensor product modules over A. This also requires a quasi-commutativity condition on the algebra and bimodules. Using this tensor product we can construct a new lifting prescription of connections to tensor product modules, generalizing the usual prescription to also include nonequivariant connections.

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Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

Cited by 10 publications

References 39 publications

Extended gravity theories from dynamical noncommutativity

Extended gravity theories from dynamical noncommutativity

Quantum gravity from noncommutative spacetime

Twist deformations of module homomorphisms and connections

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