Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity

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.

18 pages

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Cited by in corpus (12)

• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• A new perspective on Doubly Special Relativity
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Doubly special relativity as a non-local quantum field theory
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Non-local quantum field theory from doubly special relativity
• Covariant dynamics on the energy-momentum space: scalar field theory
• Towards quantum Mechanics on the curved cotangent bundle
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Formal developments in curved momentum space: the quantum field theory roadmap
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation