Lagrangian for the Frenkel electron

Abstract

We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel and BMT equations to the case of an arbitrary electromagnetic field. For a particle with anomalous magnetic moment, singularity in the relativistic equations generally occurs at the speed different from the speed of light. Detailed discussion of the ultra-relativistic motion is presented in the work: A. A. Deriglazov and W. G. Ramirez, World-line geometry probed by fast spinning particle, arXiv:1409.4756.Comment: 8 pages, close to published version: paragraph about ultra-relativistic motion is extended, the detailed discussion of this point is presented in arXiv:1409.475

Relativistic effects due to gravimagnetic moment of a rotating body

“…Many people mentioned remarkable analogies between gravitation and electromagnetism in various circumstances [16,[25][26][27][28]. Here we observe an analogy, comparing (18)- (20) with equations of motion of spinning particle (with null gyromagnetic ratio) [29] in electromagnetic field with the strength F µν…”

“…In the vector model of spin presented in [29], the configuration space consist of the position of the particle x µ (τ ), and the vector ω µ (τ ) attached to the point x µ (τ ). Minimal interaction with gravity is achieved by direct covariantization of the free action, initially formulated in Minkowski space.…”

“…of a spinning particle interacting with electromagnetic field through the gyromagnetic ratio g, see [29]. In view of this similarity, the interaction constant κ is called gravimagnetic moment [15,16], and we expect that nonminimally interacting theory with the Hamiltonian (24) could be consistent generalization of MPTD equations.…”

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

“…To introduce an interaction of spin with electromagnetic field, we use [24] the formulation (183) with the auxiliary variable 1 . We add to the action (183) the term (184) and replacė휇…”

“…The present review article is based mainly on the recent works [24][25][26][27][28][29][30][31][32][33]. In [24] we constructed final Lagrangian for a spinning particle with an arbitrary magnetic moment.…”