Multiparameter Quantum Minkowski Space-Time and Quantum Maxwell Equations Hierarchy

TL;DR

This paper generalizes quantum Minkowski space-time and Maxwell equations to a multiparameter setting using quantum group deformations, providing explicit constructions within deformed flag manifolds.

Contribution

It introduces a multiparameter quantum Minkowski space-time framework and extends the quantum Maxwell equations hierarchy using advanced quantum group techniques.

Findings

Explicit multiparameter quantum Minkowski space-time construction

Extension of quantum Maxwell equations hierarchy

Integration within deformed flag manifolds

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.