$q$-deformed Lorentz-algebra in Minkowski phase space

M. Rohregger; J. Wess

doi:doi:10.1007/s100529800960

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Particles and Fields

Eur. Phys. J. C 7, 177-183
DOI 10.1007/s100529800960

q-deformed Lorentz-algebra in Minkowski phase space

M. Rohregger¹ - J. Wess^2,3

¹ Physiologisches Institut der Ludwig-Maximilians-Universität, Pettenkoferstr. 12, D-80336 München
² Sektion Physik der Ludwig-Maximilians-Universität, Theresienstr. 37, D-80333 München
³ Max-Planck-Institut für Physik, (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 München

Received: 12 June 1998 / Published online: 5 October 1998

Abstract
In the present paper we show that the Lorentz algebra $\cal L$ as defined in [#!oschmi!#] is isomorphic to an algebra $\hat{\cal U}$ closely related to a q-deformed $SU_q(2) \otimes SU_q(2)$ algebra. On this algebra $\hat{\cal U}$ we define a Hopf algebra structure and show its action on q-spinor modules. This algebra is related to the q-deformed Minkowski space algebra by a non invertible factorisation.

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