A Deformed Poincar\'e Algebra On A Cubic Lattice
Sebastian Sachse
TL;DR
This paper introduces a deformation of the Poincaré algebra suitable for a cubic lattice, preserving the real structure and defining a deformed relativistic mass operator as a Casimir.
Contribution
It presents a novel deformation of the Poincaré algebra adapted to lattice space, maintaining key algebraic properties.
Findings
Deformation of Poincaré algebra on a cubic lattice
Deformed relativistic mass operator as a Casimir
Preservation of the real structure
Abstract
Replacing the continuous space by a cubic lattice we find a deformation of the Poincar\'e algebra. A deformation of the relativistic mass operator is shown to be a Casimir of the algebra. The real structure is preserved.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Logic