Dirac equation in the foldy-wouthuysen representation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field

1995 ◽  
Vol 105 (1) ◽  
pp. 1224-1230 ◽  
Author(s):  
A. Ya. Silenko
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
External Electromagnetic Field ◽  
Relativistic Particles

scholarly journals CLASSICAL DESCRIPTION OF SPINNING DEGREES OF FREEDOM OF RELATIVISTIC PARTICLES BY MEANS OF COMMUTING SPINORS

1999 ◽  
Vol 14 (10n11) ◽  
pp. 709-720 ◽  
Author(s):  
A. A. DERIGLAZOV ◽  
D. M. GITMAN
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Degrees Of Freedom ◽  
External Electromagnetic Field ◽  
Classical Description ◽  
Gauge Models ◽  
Higher Spin ◽  
Grassmann Variables ◽  
Higher Spins ◽  
Relativistic Particles

We consider a possibility of describing spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables xμ, ξα, χα, where ξ, χ are commuting Majorana spinors. In the course of quantization both models reproduce Dirac equation. We analyze the possibility of introducing an interaction with an external electromagnetic background into the models and generalizing them to higher spin description. The first model admits a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincaré group being generalized for higher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seems to be difficult to introduce a minimal interaction with an external electromagnetic field into this model. We compare our approach with one, which uses Grassmann variables, and establish a relation between them.

RELATIVISTIC PARTICLE WITH CURVATURE IN AN EXTERNAL ELECTROMAGNETIC FIELD

1991 ◽  
Vol 06 (22) ◽  
pp. 3989-3996 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Phase Space ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Hamiltonian Formalism ◽  
External Electromagnetic Field ◽  
Operator Form ◽  
Complete Set

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is constructed. A complete set of the constraints in the phase space is obtained and then divided into first- and second-class constraints. On this basis the canonical quantization of the model is considered. A wave equation in the operator form, resembling the Dirac equation in an external electromagnetic field, is obtained. The massless version of this model is briefly discussed.

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