Relation between Classical and Pseudo-classical Spinning Particle
نویسندگان
چکیده
The spin degrees of freedom for the relativistic particle are described by either Lorentz group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing that, appropriate constraints are constructed to put into the lagrangian. Especially a natural relation of Lorentz group variables and Grassmann variables is obtained. Hopf fibration relating the spin components to the group is just the right transformation of the spin components under Lorentz group. And with the relation just mentioned, pseudo-classical lagrangian is derived naturally from the classical one.
منابع مشابه
A Covariant Formulation of Classical Spinning Particle
Covariantly we reformulate the description of a spinning particle in terms of the Poincaré group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame an...
متن کاملPolyakov’s Spin Factor for a Classical Spinning Particle via BRST Invariant Path Integral
For the ‘classical’ formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization invariance and ‘quasi-supersymmetry’. In the path integral, the BRST invariant Lagrangian is used and the same spin factor is obtained as in the pseudo-classica...
متن کاملDerivation of the Classical Lagrangian for the Relativistic Spinning Particle
The ‘classical’ model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic rotator. Furthermore, the variables tμ corresponding to the ψ ∗ of the ‘pseudo-classical’ model, are necessary for the covariant formulation. The dynamical ...
متن کاملSpinning Particles in General Relativity
— We analyze the behavior of a spinning particle in gravity, both from a quantum and a classical point of view. We infer that, since the interaction between the space-time curvature and a spinning test particle is expected, then the main features of such an interaction can get light on which degrees of freedom have physical meaning in a quantum gravity theory with fermions. Finally, the dimensi...
متن کاملSpinning Particles in Taub-nut Space
The geodesic motion of pseudo-classical spinning particles in Euclidean Taub-NUT space is analysed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected. PACS number(s): 04.20.Jb, 02.40.-K The con guration space of spinning particles (spinning space) is an supersymmetric extension of an ordinary Riemannian manifold, para...
متن کامل