Lorentz Transformations and Covariance of the Dirac Equation

2004 ◽  
pp. 131-154
Author(s):  
Franz Schwabl
Keyword(s):  
Dirac Equation ◽  
Lorentz Transformations

scholarly journals QUANTUM STATE OF A FREE SPIN-½ PARTICLE AND THE INEXTRICABLE DEPENDENCE OF SPIN AND MOMENTUM UNDER LORENTZ TRANSFORMATIONS

2012 ◽  
Vol 10 (04) ◽  
pp. 1230003 ◽  
Author(s):  
TIAGO DEBARBA ◽  
REINALDO O. VIANNA
Keyword(s):  
Dirac Equation ◽  
Quantum State ◽  
Free Particle ◽  
Lorentz Transformations ◽  
Spin Particle ◽  
Quantization Axis ◽  
Spin Quantization

We revise the Dirac equation for a free particle and investigate Lorentz transformations on spinors. We study how the spin quantization axis changes under Lorentz transformations, and evince the interplay between spin and momentum in this context.

Dirac Theory of the Electron

2019 ◽  
pp. 401-416
Author(s):  
P.J.E. Peebles
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Dirac Equation ◽  
Magnetic Dipole Moment ◽  
Orbit Interaction ◽  
Gyromagnetic Ratio ◽  
Lorentz Transformations ◽  
Spin Orbit ◽  
Dirac Theory ◽  
Quantum Treatment

This chapter explores applications drawn from Dirac theory of the electron. In the treatment of electrons, it uses the following: an electron has spin 1/2; its magnetic dipole moment is very nearly twice that of the orbital model in which charge and mass move together; and the spin-orbit interaction is a factor of two off the value arrived at by the heuristic argument in the Chapter 7. The factor of two in the last effect is recovered if one does the Lorentz transformations in a more careful (and correct) way, but it is easier to get it from the relativistic Dirac equation. This equation applied to an electron also says the particle has spin 1/2, as observed, and it says the gyromagnetic ratio in equation (23.11) is g = 2. The small difference from the observed value is accounted for by the quantum treatment of the electromagnetic field.

scholarly journals Tachyonic Dirac Equation Revisited

2020 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
Dirac Equation ◽  
Charge Conjugation ◽  
The Other ◽  
Lorentz Transformations ◽  
Mathematical Tool ◽  
Classical Dynamics ◽  
Theory Of Relativity ◽  
Theoretical Approaches ◽  
Covariant Equation ◽  
The Mean

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

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