Covariant hamiltonian spin dynamics in curved space-time (original) (raw)
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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 Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coo...
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We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.
Spin on a curved spacetime with absolute time
We present a new covariant approach to the quantum mechanics of a charged 1/2-spin particle in given electromagnetic and gravitational fields. The background space is assumed to be a curved Galileian spacetime, that is a curved spacetime with absolute time. This setting is intended both as a suitable approximation for the case of low speeds and feeble gravitational fields, and as a guide for eventual extension to fully Einstenian space-time. Moreover, in the flat spacetime case one completely recovers standard non-relativistic quantum mechanics.
Quantum mechanics of a spin particle in a curved spacetime with absolute time
Reports on Mathematical Physics, 1995
We present a new covariant approach to the quantum mechanics of a charged 1/2-spin particle in given electromagnetic and gravitational fields. The background space is assumed to be a curved Galileian spacetime, that is a curved spacetime with absolute time. This setting is intended both as a suitable approximation for the case of low speeds and feeble gravitational fields, and as a guide for eventual extension to fully Einstenian space-time. Moreover, in the flat spacetime case one completely recovers standard nonrelativistic quantum mechanics.
Spinning particles in general relativity
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A lagranglan which leads to the standard equations for a spinning particle in a gravitational field (with torsion) is presented. It, leads to the correct grawtational field equations as well. For zero gravatatlonal field, the present approach gives a lagrangian description for any unitary irreducible representation of the connected Poincar~ group.
Canonical formulation for a non-relativistic spinning particle coupled to gravity
Classical and Quantum Gravity
We systematically derive an action for a nonrelativistic spinning particle in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the corresponding action in a curved background. It is achieved by following our recently developed technique of localising the flat space Galilean symmetry (Banerjee et al 2014 Phys. Lett. B 737 369; Banerjee et al 2015 Phys. Rev. D 91 084021; Banerjee et al 2015 Class. Quantum Grav. 32 045010). The coupling of the spinning particle to a Newton–Cartan background is obtained naturally. The equation of motion is found to differ from the geodesic equation, in agreement with earlier findings. Results for both the flat space limit and the spinless theory (in curved background) are reproduced. Specifically, the geodesic equation is also obtained in the latter case.
Spinning bodies in curved spacetime
Physical Review D, 2016
We study the motion of neutral and charged spinning bodies in curved spacetime in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation that allows for different choices of the Hamiltonian. We derive conditions for the existence of constants of motion and apply the formalism to the case of spherically symmetric spacetimes. We show that the periastron of a spinning body in a stable orbit in a Schwarzschild or Reissner-Nordstrøm background not only precesses but also varies radially. By analyzing the stability conditions for circular motion we find the innermost stable circular orbit (ISCO) as a function of spin. It turns out that there is an absolute lower limit on the ISCOs for increasing prograde spin. Finally we establish that the equations of motion can also be derived from the Einstein equations using an appropriate energy-momentum tensor for spinning particles.