Baxter operators for arbitrary spin II

This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional s?₂ representations. We consider the Baxter operators used in Bazhanov et al. (1996, 1997, 1999, 2010) [1] and [2], formulate their construction uniformly with the construction of our previous paper. The building blocks of all global chain operators are derived from the general Yang-Baxter operators and all operator relations are derived from general Yang-Baxter relations. This leads naturally to the comparison of both constructions and allows to connect closely the treatment of the cases of infinite-dimensional representation of generic spin and finite-dimensional representations of integer or half-integer spin. We prove not only the relations between the operators but present also their explicit forms and expressions for their action on polynomials representing the quantum states.     

Projection operators and supplementary conditions for superfields with arbitrary spin

It is shown that a superfield with an external spin j and a non-vanishing mass contains four irreducible representations of the supersymmetry algebra. A general method is proposed for extracting these irreducible multiplets out of the superfield using projection operators constructed with the help of Casimir operators. The same decomposition is expressed in terms of supplementary differential conditions.     

Baxter operators with deformed symmetry

Baxter operators are constructed for quantum spin chains with deformed _s?2${\mathrm{s?}}_2$ symmetry. The parallel treatment of Yang–Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.     

Spin squeezing inequalities for arbitrary spin

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.     

Order and disorder operators of the Baxter model

We complete the construction of order and disorder operators of the Baxter model along the lines of a previous paper.     

Feynman propagator for an arbitrary half—integral spin

Based on the solution to Bargmann－Wigner equation for a particle with arbitrary half-integral spin, a direct derivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the general commutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitrary half-integral spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.     

自旋为任意整数的传播子

以自旋为任意整数的自由粒子的波函数(Bargmann-Wigner方程的解)为基础，进一步研究了 自旋为任意整数的投影算符和传播子.证明了Behrends和Fronsdal所构造的投影算符是正确 的.导出了自旋为任意整数的场的一般对易规则和费恩曼传播子的一般表达式. 关键词： 整数自旋 投影算符 对易规则 费恩曼传播子     

GKS inequalities for arbitrary spin ising ferromagnets

Elementary proofs of the first and second Griffiths-Kelly-Sherman (GKS) inequalities are given for higher-spin Ising systems with a Hamiltonian containing only a quadratic form in the spin variables and integer powers of single spin variables. These proofs are obtained using Gaussian random variables. A slight generalization of previous results has been obtained in that the coefficients of the even powers of the spin variables are allowed to be negative.Work supported by NSF Grant GP-36564X.     

Feynman propagator for a particle with arbitrary spin

Based on the solution to the Rarita-Schwinger equations, a direct derivation of the projection operator and propagator for a particle with arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin; the general commutation rules and Feynman propagator for a free particle of any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, 4 are provided.Received: 13 March 2003, Revised: 24 April 2005, Published online: 6 July 2005     

Thermodynamic duality for classical systems of arbitrary spin

Given a classical spins system, namely, a set of spin sites of maximum spins inv-dimensional space along with a Hamiltonian defined on the possible spin configurations, a general method is described for constructing a large class of dual lattices of the same spin. The method utilizes the commutative group structure with which the configuration space is endowed.On leave from: Department of Mathematics, Indiana University, Bloomington, Indiana.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Wigner functions for two arbitrary operators and spectrum perturbation

We have concentrated on the Wigner function for the photon number and a quadrature operator, which we find to differ from zero outside the spectrum of the photon number operator. We have provided an illustration with a coherent state.     

Zitterbewegung of particles with arbitrary spin

The existence of zitterbewegung of particles with higher spins (s≥1) is proved. The investigation is based on the idea of Curie, Jordan, and Sudarshan that there are two aspects of relativistic invariance and also on the determination of the dynamical variables that describe systems with arbitrary spin obtained by Jordan and Mukunda. A number of new paradoxical properties of zitterbewegung unknown in Dirac theory is revealed. For example, particles with high spins (s≥1) can have a velocity greater than light. It is shown in a general form that elimination of zitterbewegung in all directions of space, or even only in a plane, is impossible. There can be only partial liquidation of zitterbewegung, in one of the directions of space, and then only at the price of violation of relativistic invariance of the theory. Finally, it is suggested that the paradoxical properties of zitterbewegung can be understood by redefining the momentum and mass operators. In this way, a connection between zitterbewgung and tachyons is established.     

Interacting Bhabha field with arbitrary spin

The Bhabha equation which describes a particle having multi-mass and spin states with maximum spin S, integer or half an odd integer, is considered. In the presence of interactions e.g. the electromagnetic interaction introduced through minimal coupling, it is found to yield the same (anti-) commutators as in the case of a free field. Also the propagation of an interacting field is causal. This shows the absence of inconsistencies of the type, pointed out by Johnson and Sudarshan. Finally the applicability of the methods of quantisation is discussed.     

Quantum nonlinear sigma model for arbitrary spin Heisenberg antiferromagnets

We derive a quantum nonlinear sigma model (QNLSM) for quantum Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit of the low temperature is naturally carried out for the reliability of the QNLSM. The S dependence of the effective coupling constant and the spin-wave velocity in the QNLSM are also obtained explicitly. The resulting spin-wave velocity for 2D spin-1/2 QHA highly concurs with the experimental data of high T(c) compound La(2)CuO(4). The predicted correlation lengths for 2D QHA and spin-gap magnitudes for 1D QHA also agrees with the accurate numerical results.     

Conformal invariance of relativistic equations for arbitrary spin particles

We show that any Poincaré-invariant equation for particles of zero mass and of discrete spin provide a unitary representation of the conformal group, and find an explicit expression of the conformal group generators in terms of Poincaré group generators.