Deformed phase spaces with group valued momenta

Arzano, Michele; Nettel, Francisco

doi:10.1103/physrevd.94.085004

Cited by 5 publications

(4 citation statements)

References 78 publications

(121 reference statements)

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“…A peculiar feature of models of deformed kinematics based on a momentum group manifold is the non-abelian composition of four-momenta inherited from the group multiplication law. As argued in [38] such composition law reflects the way momenta, seen as quantum numbers, add for multiparticle states. As for Lorentz transformations and mass Casimir, the explicit form of the composition law depends on the choice of coordinates for the momentum manifold.…”

Section: Composition Of Momentamentioning

confidence: 90%

UV dimensional reduction to two from group valued momenta

Arzano

Nettel

2017

Physics Letters B

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We describe a new model of deformed relativistic kinematics based on the group manifold $U(1) \times SU(2)$ as a four-momentum space. We discuss the action of the Lorentz group on such space and and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by {\it two} energy scales $\lambda$ and $\kappa$. A relevant feature of the model is that it exhibits a running spectral dimension $d_s$ with the characteristic short distance reduction to $d_s =2$ found in most quantum gravity scenarios.Comment: 15 pages, 1 figur

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Section: Composition Of Momentamentioning

confidence: 90%

UV dimensional reduction to two from group valued momenta

Arzano

Nettel

2017

Physics Letters B

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“…Deformed quantum phase spaces are constantly studied with a number of interesting papers appearing recently, like e.g. [14].…”

Section: Introductionmentioning

confidence: 99%

Twisted bialgebroids versus bialgebroids from a Drinfeld twist

Borowiec

Pachoł

2017

J. Phys. A: Math. Theor.

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Bialgebroids (resp. Hopf algebroids) are bialgebras (Hopf algebras) over noncommutative rings. Drinfeld twist techniques are particularly useful in the (deformation) quantization of Lie algebras as well as underlying module algebras (=quantum spaces). Smash product construction combines these two into the new algebra which, in fact, does not depend on the twist. However, we can turn it into bialgebroid in the twist dependent way. Alternatively, one can use Drinfeld twist techniques in a category of bialgebroids. We show that both techniques indicated in the title: twisting of a bialgebroid or constructing a bialgebroid from the twisted bialgebra give rise to the same result in the case of normalized cocycle twist. This can be useful for better description of a quantum deformed phase space. We argue that within this bialgebroid framework one can justify the use of deformed coordinates (i.e. spacetime noncommutativity) which are frequently postulated in order to explain quantum gravity effects.

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“…In this respect, Arzano and Nettel [18] in 2016 introduced a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bialgebras, they developed tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group.…”

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confidence: 99%

“…These tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the n-dimensional generalization of the κ-deformed momentum space and the SL(2, R) momentum space in three space-time dimensions. They also discussed classical momentum observables associated to multiparticle systems and argued that these combined according the usual four-vector addition despite the non-Abelian group structure of momentum space (see [18] for further information).…”

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confidence: 99%