相关论文: Physics and Mathematics of Calogero particles
Several topics related to quantum spin models of Calogero-Sutherland type, partially solvable spin chains and Polychronakos's "freezing trick" are rigorously studied.
We show that the model of discrete spaces that we have proposed in previous contributions gives a comprehensive and detailed interpretation of the properties of the standard model of particles. Moreover the model also suggests the possible…
Matrix generalizations of the N-particle quantum-mechanical Calogero model classifying according to representations of the symmetric group $S_N$ are considered. Symmetry properties of the eigen-wave functions in the matrix Calogero models…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
We construct a class of interacting spin Calogero-Moser type systems. They can be regarded as a many particle system with spin degrees of freedom and as an integrable spin chain of Gaudin type. We prove that these Hamiltonian systems are…
The physics case for axions and axion-like particles is reviewed and an overview of ongoing and near-future laboratory searches is presented.
We briefly review models of relativistic particles with spin. Departing from the oldest attempts to describe the spin within the lagrangian framework we pass through various non supersymmetric models. Then the component and superfield…
We construct new realizations of the Virasoro algebra inspired by the Calogero model. The Virasoro algebra we find acts as a kind of spectrum-generating algebra of the Calogero model. We furthermore present the superextension of these…
We compute the symplectic structure of the spin Calogero model in terms of algebro-geometric data on the associated spectral curve.
In a previous paper, we introduce a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter. Here the main purpose is to give explicit solutions of several factorization…
We extend our previous analysis of the classical integrable models of Calogero in several respects. Firstly we provide the algebraic resaons of their quantum integrability.Secondly we show why these systems allow their initial value problem…
The classical and the quantum motion of a massive body in the rotating tube is considered. Photon is included. The spin motion described by the Bargmann-Michel-Telegdi equation is considered in the rotation tube and rotating system.
The complete solutions of the spin generalization of the elliptic Calogero Moser systems are constructed. They are expressed in terms of Riemann theta-functions. The analoguous constructions for the trigonometric and rational cases are also…
Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the $sL(2,\rr)$ structure of the Calogero--Moser wave…
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on…
We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…
We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the…
We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type…
This study presents standard Cliffordian Kaehler analogue of Lagrangian mechanics. Also, the some geometric and physical results related to the standard Cliffordian Kaehler dynamical systems are given.