New quantum Poincaré algebra and κ-deformed field theory

Abstract

We derive a new real quantum Poincare algebra with standard real structure, obtained by contraction ofUq(0(3, 2)) (q real) , which is a standard real Hopf algebra, depending on a dimension-full parameter K instead of q. For our real quantum Poincare algebra both Casimirs are given. The free scalar K-deformed quantum field theory is considered. it appears that the K-parameter introduced nonlocal q-time derivatives with In q-1 /K.

On κ-deformation and triangular quasibialgebra structure

“…The κ-Poincaré Hopf algebra U κ (P) [1][2][3] is a deformation of (the universal enveloping algebra of) the Poincaré algebra, with the strength of the deformation being governed by a parameter κ with units of mass [4,5]. This paper is a continuation of earlier work [6,7], following [8], whose aim is systematically to construct κ-deformed quantum field theory from the following particular perspective.…”

Covariant particle exchange for κ-deformed theories in dimensions

“…The Algebra U κ (P ) For the present purposes it is most convenient to work in the original basis of [1,2], rather than the bicrossproduct basis subsequently found in [3]. In the original basis the two-dimensional κ-Poincaré algebra U κ (P ) is defined by 1) where N is the generator of boosts and P µ , µ = 1, 2, are the momentum generators.…”

“…In the original basis the two-dimensional κ-Poincaré algebra U κ (P ) is defined by 1) where N is the generator of boosts and P µ , µ = 1, 2, are the momentum generators. The coalgebra is given by…”

“…The universal enveloping algebra U(P ) of the Poincaré algebra is known to possess a family of deformations U κ (P ), with U ∞ (P ) = U(P ) (1.1) parameterized by a mass scale κ [1,2,3]. From the dual point of view, in the Hopf-algebraic sense [4], there is a κ-deformation of the algebra of functions on the Poincaré group [5].…”

On the classification of quantum Poincaré groups

“…Remembering that β ∈ {1, −1, i, −i}, q = ±i, we get q = ±1. Thus we can (and will) omit L 3 , L 4 . We obtain β = q, i = j or β = −q, i = j (q ∈ {1, −1}, i, j ∈ {1, 2}).…”