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Register a new userQuantum Deformation of the Poincare Supergroup and $kappa$-deformed Superspace
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P. Kosi{n}ski
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The classical $r$-matrix for $N=1$ superPoincar{e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{e} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{e} group with the deformation parameter $q$ described by fundamental mass parameter $kappa quad (kappa^{-1}=ln{q})$. The $kappa$-deformation of $N=1$ superspace as dual to the $kappa$-deformed supersymmetry algebra is discussed.
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In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.
We describe the deformed E.T. quantization rules for kappa-deformed free quantum fields, and relate these rules with the kappa-deformed algebra of field oscillators.
In this short note, based on the talk given at the 3rd Conference of the Polish Society on Relativity, I present the basic points of our recent paper Symmetries of quantum spacetime in three dimensions, stressing their physical meaning, and avoiding technical details.
There is a growing number of physical models, like point particle(s) in 2+1 gravity or Doubly Special Relativity, in which the space of momenta is curved, de Sitter space. We show that for such models the algebra of space-time symmetries possesses a natural Hopf algebra structure. It turns out that this algebra is just the quantum $kappa$-Poincare algebra.
We present the quantum $kappa$-deformation of BMS symmetry, by generalizing the lightlike $kappa$-Poincare Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $kappa$-deformation of Poincare algebra is given by a twist and the lightlike deformation of any algebra containing Poincare as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained $kappa$-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.
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