Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity

Abstract

We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: A) One-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic {\it Zitterbewegung}; B) Spin-induced non commutativity and the problem of covariant formalism; C) Three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; D) Paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultra relativistic limit, and equations with improved behavior.

Invited review article for the Journal "Advances in Mathematical Physics". Based on the recent works: arXiv:1312.6247, arXiv:1406.6715, arXiv:1409.4756, arXiv:1509.05357, arXiv:1511.00645, arXiv:1609.00043. 61 pages, 3 figures

References in corpus (17)

• The Confrontation between General Relativity and Experiment
• Muon g-2: Review of Theory and Experiment
• Magnetoresistance due to edge spin accumulation
• Twisted electron in a strong laser wave
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Lagrangian for the Frenkel electron
• Spin and localization of relativistic fermions and uncertainty relations
• Spin supplementary conditions for spinning compact binaries
• World-line geometry probed by fast spinning particle
• Probing deformed quantum commutators
• Antigravity: Spin-gravity coupling in action
• Quantum gravitational corrections for spinning particles
• Polymer quantization versus the Snyder noncommutative space
• Fast Evolution and Waveform Generator for Extreme-Mass-Ratio Inspirals in Equatorial-Circular Orbits
• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
• Photon emission of extremal Kerr-Newman black holes
• Generalized twist deformations of Poincare and Galilei quantum groups

Cited by in corpus (5)

• Spinning test particles in the $\gamma$ spacetime
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• Non-commutative black holes of various genera in the connection formalism
• Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin
• Comment on "Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field" by C. H. McGruder III