相关论文: Spin and Statistics in Classical Mechanics
The kinematic degrees of freedom of spinning particles are analyzed and an explicit construction of the phase space and the simplectic structure that accomodates them is presented. A Poincare invariant theory of classical spinning particles…
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a…
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non compact subgroups is straightforward. As a by-product parametrizations of the same…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
Although there are many proposals of relativistic spin observables, there is no agreement about the adequate definition of this quantity. This problem arises from the fact that, in the present literature, there is no consensus concerning…
We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian…
We examine the construction of the spin angular momentum in systems with pseudoclassical Grassmann variables. In constrained systems there are many different algebraic forms for the dynamical variables that will all agree on the constraint…
The twist-deformation of the Poincar\'e algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and…
The relation between Einstein gravity and the Chern-Simons gauge theory of the Poincare' group is discussed at the classical level.
We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass…
We consider a possibility to describe spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables $x^\mu,\xi_\alpha,\chi_\alpha$, where $\xi,\chi$…
A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J…