Twist-related geometries on q-Minkowski space
P.P.Kulish, A.I.Mudrov
TL;DR
This paper explores how twist deformations of the Lorentz algebra influence the structure of quantum Minkowski space, focusing on the formulation of fundamental equations like Klein-Gordon-Fock and Dirac in this non-commutative setting.
Contribution
It introduces a twist-based approach to quantum Minkowski space and derives deformed Klein-Gordon-Fock and Dirac equations within this framework.
Findings
Derived twisted Klein-Gordon-Fock and Dirac equations on quantum Minkowski space.
Analyzed the impact of Cartan subalgebra twist on space-time symmetries.
Provided insights into non-commutative geometry of quantum space-time.
Abstract
The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the twist theory the Klein-Gordon-Fock and Dirac equations on the quantum Minkowski space are studied from this point of view for the simplest quantum deformation of the Lorentz algebra induced by its Cartan subalgebra twist.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra