Abstract
We derive a new real quantum Poincaré algebra with standard real structure, obtained by contraction of U q (O(3,2)) ( q real), which is a standard real Hopf algebra, depending on a dimension-full parameter κ instead of q. For our real quantum Poincaré algebra both Casimirs are given. The free scalar κ-deformed quantum field theory is considered, it appears that the κ-parameter introduced nonlocal q ̃ - time derivatives with ln q ̃ ∼ 1 κ .
Highlights
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
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
We found in ref. [2] that only two provide examples of real forms of U q( Sp (4; IC )) suitable for our contraction procedure to quantum the Poincare algebra tti _ these two real forms were described by nonstandard involutions
Summary
The commutation relations for two tilded generators can be obtained from the formulae in ref. Calculation of coproducts for physical generators requires the knowledge of the following formulae: A(e3) = e3 ®qh,12 + q-h3120e3 + (q-1-q)q-h1/2e2®ei qh212, A(e_3) = e_3 ®qh,12 + q-h3120e_3. Coproducts of the antipode-extended Cartan-Weyl basis and the definitions (2.11) we can write the qdeformation of the 0 ( 3, 2) Lie algebra as well as the coproduct relations for the q-deformed 0 ( 3, 2) generators. (ii) We perform further the quantum de-Sitter contraction, obtained by the conventional rescaling of the 0(3, 2) rotation generators. (b) Boosts sector 0(3, 1) (L± =M14 ±iM24, L3= M34). The contraction to standard real quantum Poincare algebra. In order to obtain our new q-Poincare algebra we proceed further as follows:. ( c) Translations sector (P ± =P2 ± iPi, P3, P0 ).
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