q-Euclidean space and quantum group wick rotation by twisting

Details q-Euclidean space and quantum group wick rotation by twisting q-Euclidean space and quantum group wick rotation by twisting

1994-01-23

arxiv.org/abs/hep-th/9401112v1

J.Math.Phys. 35 (1994) 5025-5034

Physics

High Energy Physics

High Energy Physics - Theory

16 pages

Scientific paper

10.1063/1.530828

We study the quantum matrix algebra $R_{21}x_1x_2=x_2x_1 R$ and for the standard $2\times 2$ case propose it for the co-ordinates of $q$-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices $M_q(2)$ but in a form which is naturally covariant under the Euclidean rotations $SU_q(2)\otimes SU_q(2)$. We also introduce a quantum Wick rotation that twists this system precisely into the approach to $q$-Minkowski space based on braided-matrices and their associated spinorial $q$-Lorentz group.

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