Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations

Abstract

We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning particle with gravity. We shortly discuss some novel properties deduced from the Lagrangian form of MPTD-equations: emergence of an effective metric instead of the original one, non-commutativity of coordinates of representative point of the body, spin corrections to Newton potential due to the effective metric as well as spin corrections to the expression for integrals of motion of a given isometry.

12 pages, misprints corrected, references added, close to published version, according to the referee's suggestions

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• Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in ultra-relativistic regime and gravimagnetic moment
• Ultra-relativistic spinning particle and a rotating body in external fields
• Modified teleparallel gravity with higher-derivative torsion terms
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• Complete set of quasi-conserved quantities for spinning particles around Kerr
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• Quantum gravitational corrections for spinning particles
• Quantum corrections for spinning particles in de Sitter
• Noncommutative Geometry and Fluid Dynamics
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• The Relativistic Spherical Top as a Massive Twistor
• Spinning gravimagnetic particles in Schwarzschild-like black holes
• Influence of gravitational waves on circular moving particles
• An overview of the gravitational spin Hall effect
• Spin dynamics of moving bodies in rotating black hole spacetimes
• Revisiting the dynamics of a charged spinning body in curved spacetime
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation
• Generalized Mathisson-Papapetrou-Tulczyjew-Dixon Equations
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Spinning test particles in the spacetime of a global monopole