Geometrizing the Klein-Gordon and Dirac equations in doubly special relativity. (English) Zbl 1518.83001
Summary: 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.
MSC:
| 83A05 | Special relativity |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 53Z05 | Applications of differential geometry to physics |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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