Asymmetric particle-antiparticle Dirac equation: first quantization

Abstract

We derive a Dirac-like equation, the asymmetric Dirac equation, where particles and antiparticles sharing the same wave number have different energies and momenta. We show that this equation is Lorentz covariant under proper Lorentz transformations (boosts and spatial rotations) and also determine the corresponding transformation law for its wave function. We obtain a formal connection between the asymmetric Dirac equation and the standard Dirac equation and we show that by properly adjusting the free parameters of the present wave equation we can make it reproduce the predictions of the usual Dirac equation. We show that the rest mass of a particle in the theoretical framework of the asymmetric Dirac equation is a function of a set of four parameters, which are relativistic invariants under proper Lorentz transformations. These four parameters are the analog to the mass that appears in the standard Dirac equation. We prove that in order to guarantee the covariance of the asymmetric Dirac equation under parity and time reversal operations (improper Lorentz transformations) as well as under the charge conjugation operation, these four parameters change sign in exactly the same way as the four components of a four-vector. The mass, though, being a function of the square of those parameters remains an invariant. We also extensively study the free particle plane wave solutions to the asymmetric Dirac equation and derive its energy, helicity, and spin projection operators as well as several Gordon's identities. The hydrogen atom is solved in the present context after applying the minimal coupling prescription to the asymmetric Dirac equation, which also allows us to appropriately obtain its non-relativistic limit.

27 pages, no figures, double column, RevTex4; v2: published version

References in corpus (8)

• Evading quantum mechanics
• S_4 Flavored CP Symmetry for Neutrinos
• Information-Entropic for Travelling Solitons in Lorentz and CPT Breaking Systems
• Lorentz violating extension of the Standard Model and the Beta-decay end-point
• Baryogenesis in Lorentz-violating gravity theories
• Lorentz-violating dilatations in the momentum space and some extensions on non-linear actions of Lorentz algebra-preserving systems
• A relativistic electron in an anisotropic conduction band
• Asymmetric particle-antiparticle Dirac equation: second quantization

Cited by in corpus (2)

• Galilean relativity and wave-particle duality imply the Schrödinger equation
• Asymmetric particle-antiparticle Dirac equation: second quantization