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arXiv · 1612.05034

Multiparameter Quantum Minkowski Space-Time and Quantum Maxwell Equations Hierarchy

V. K. Dobrev
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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, $z,\bar z$. Weproposed also new $q$ - Minkowski coordinates which together with $z,\bar z$ 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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V. K. Dobrev. 2016-12-15. Multiparameter Quantum Minkowski Space-Time and Quantum Maxwell Equations Hierarchy. https://arxiv.org/abs/1612.05034

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