q-Deformed Relativistic Wave Equations
Mathias Pillin (Max-Planck-Institut fuer Physik,, Werner-Heisenberg-Institut, Foehringer Ring 6, D-80805 Muenchen, Germany)
TL;DR
This paper constructs $q$-deformed relativistic wave equations, including Dirac, Proca, Rarita-Schwinger, and Maxwell equations, using the representation theory of $q$-deformed Lorentz and Poincaré symmetries, addressing the one-particle problem in this framework.
Contribution
It introduces explicit $q$-deformed relativistic wave equations based on non-commutative Minkowski space, extending classical equations with a new algebraic structure.
Findings
$q$-deformed wave operators resemble classical ones structurally
Explicit forms of $q$-deformed Dirac, Proca, Rarita-Schwinger, Maxwell equations
Addresses the $q$-deformed one-particle relativistic problem
Abstract
Based on the representation theory of the -deformed Lorentz and Poincar\'e symmeties -deformed relativistic wave equation are constructed. The most important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations are treated explicitly. The -deformed wave operators look structurally like the undeformed ones but they consist of the generators of a non-commu\-ta\-tive Minkowski space. The existence of the -deformed wave equations together with previous existence of the -deformed wave equations together with previous results on the representation theory of the -deformed Poincar\'e symmetry solve the -deformed relativistic one particle problem.
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