Bulg. J. Phys. vol.44 no.1 (2017), pp. 031-038

Multiparameter Quantum Minkowski Space-Time and Quantum Maxwell Equations Hierarchy

V.K. Dobrev
Institute for Nuclear Research and Nuclear Energy,\\ Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
Abstract. Earlier we have proposed new q-Maxwell equations which are the first members of an infinite new hierarchy of q-difference equations. We have used an indexless formulation in which all indices are traded for two conjugate variables, z,̅z. We proposed also new q-Minkowski coordinates which together with z,̅z can be interpreted as the six local coordinates of a SU_q(2,2) flag manifold. In the present paper we generalise the main ingredients of this construction to the multiparameter case using the seven-parameter quantum group deformation of GL(4) and U(gl(4)) and the four-parameter quantum group deformation of SL(4) and U(sl(4)). The main result is the explicit presentation of the multiparameter quantum Minkowski space-time within the corresponding deformed flag manifold.

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