Geometrizing the Klein–Gordon and Dirac equations in doubly special relativity
S. A. Franchino-Viñas, J. J. Relancio
Abstract
Abstract In this work we discuss the deformed relativistic wave equations, namely the Klein–Gordon and Dirac equations in a doubly special relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein–Gordon case.
Topics & Concepts
PhysicsDirac (video compression format)Klein–Gordon equationGeneral relativityMathematical physicsRelativistic wave equationsDirac equationAlgebraic numberHomogeneous spaceDirac algebraTheory of relativitySpace (punctuation)Hilbert spaceClassical mechanicsTheoretical physicsQuantum mechanicsMathematical analysisGeometryMathematicsNonlinear systemLinguisticsNeutrinoPhilosophyNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsAdvanced Differential Geometry Research