Asymmetric particle-antiparticle Dirac equation: first quantization,Journal of Physics G: Nuclear and Particle Physics

当前位置： X-MOL 学术 › J. Phys. G Nucl. Partic. Phys. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Asymmetric particle-antiparticle Dirac equation: first quantization
Journal of Physics G: Nuclear and Particle Physics ( IF 3.5 ) Pub Date : 2023-11-24 , DOI: 10.1088/1361-6471/ad0312
Gustavo Rigolin

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.

更新日期：2023-11-24

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文

全部期刊列表>>