Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable

Abstract

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with complicated structure of constraints. In this work we describe and discuss the spin fiber bundle which appeared in various mechanical models where spin is described by vector-like variable.

References in corpus (4)

• Lagrangian for Frenkel electron and position's non-commutativity due to spin
• Frenkel electron and a spinning body in a curved background
• Classical-mechanical models without observable trajectories and the Dirac electron
• Non-Grassmann mechanical model of the Dirac equation

Cited by in corpus (12)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
• Lagrangian for Frenkel electron and position's non-commutativity due to spin
• Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Frenkel electron and a spinning body in a curved background
• Ultra-relativistic spinning particle and a rotating body in external fields
• Lagrangian for the Frenkel electron
• Reparametrization Invariance and Some of the Key Properties of Physical Systems
• A Bilocal Model for the Relativistic Spinning Particle
• Spinning gravimagnetic particles in Schwarzschild-like black holes
• To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models