Arbitrary Integer Spin Research Articles

Gauge symmetries in three dimensions

A non-lagrangian approach to gauge symmetries in three dimensions is discussed. The general construction of Lorentz-covariant and local fields carrying massive particles of arbitrary integer spin is presented. The “minimal” fields for integer spin are explicitly constructed. Following Weinberg's analysis in the 4D case it is shown that the gauge symmetry results from the group-theoretical considerations and the condition that there should exist a long-range interaction.

Complete analysis of two spin correlations of valence bond solid chains for all integer spins

For the valence bond solid (VBS) chain ground state introduced by Affleck et al. we evaluate exactly all 2S two-point correlation functions for all integer spinsS with a simple transfer matrix method. These correlations are expectation values of 2S different two-site irreducible tensor operators also presented in this article. Each of the firstS correlations exhibits its own purely exponential decay whereas the others vanish. It turns out that in the largeS limit there are both very large and very short ranged correlations. We use the correlation functions to calculate the probabilities that two spins at distancer add up to total spin σ and also derive a formula for the probability that two spins at distancer enclose an angle Θ. This provides a complete and perspecuate description of the VBS state for arbitrary integer spinS.

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF INTEGER SPIN

We present a method based on BRST techniques for how to obtain the conventional equations for symmetric tensor gauge fields which describe free massless particles of arbitrary integer spin. We do so in a wave function representation in a flat space-time background of any dimension. A fairly straightforward way is also presented for how to obtain the equations from a gauge invariant Lagrangian of the form [Formula: see text].

Conformal invariance and the operator content of the XXZ model with arbitrary spin

The authors are concerned with the critical properties of the anisotropic Heisenberg chain, or XXZ model, with arbitrary integer or half-integer spin. The eigenspectra of these Hamiltonians, with periodic boundaries, are calculated for finite chains by solving numerically their associated Bethe ansatz equations. The resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified, for lattices with an even and odd number of sites. The results for spin 1 and spin 3/2 indicate that the conformal anomaly c for these models, in the gapless regime, has the value c=3S/(1+S), independent of the anisotropy, and the exponents vary continuously with the anisotropy as in the eight-vertex model. The operator content of these models indicate that the underlying field theory governing these critical spin-S models is described by composite fields formed by the product of Gaussian and Z(N) fields, with N=2S. Finally some of the irrelevant operators which produce the leading finite-size corrections of the eigenenergies are identified.

Current conservation as a geometric property of space–time

Working within the framework of stochastic quantum mechanics, we prove that a mild reality constraint on the radial part of the resolution generator renders the (probability) current, for a single particle with only positive (or only negative) energies and having arbitrary integer spin, conserved. The result is proven both nonrelativistically and relativistically. This extends some earlier results that had been obtained for spinless systems. We argue that the origin of such a conservation law is a consequence of the particular geometry of space–time predicated by the formalism of stochastic quantum mechanics.

On massive fermions and bosons in galactic halos

Galactic halos of massive fermions, of arbitrary half integer spin, or of massive bosons are considered. To give results of astrophysical interest, the fermions with spin s should have a mass m ∼- 10 eV/c 2/(2s + 1) 1 4 , while the bosons a mass in the range from 10 eV/ c 2 to 10 −24eV/ c 2. We also consider galactic halos of more than one fermion species.

Systematics of higher-spin gauge fields

Free-field theories for symmetric tensor and tensor-spinor gauge fields have recently been obtained which describe massless particles of arbitrary integer or half-integer spin. An independent discussion of these field theories is given here, based on a hierarchy of generalized Christoffel symbols with simple gauge transformation properties. The necessity of certain constraints on gauge fields and parameters is easily seen. Wave equations and Lagrangians are expressed in terms of the Christoffel symbols, and the independent modes of the system are counted in covariant gauges. Minimal-coupling inconsistency and a combined system of higher-spin boson gauge fields interacting with relativistic particles is discussed.

Nonspherical Perturbations of Relativistic Gravitational Collapse. II. Integer-Spin, Zero-Rest-Mass Fields

A nearly spherical star collapses through its gravitational radius. Nonspherical perturbations exist in its density, pressure, electromagnetic field, and gravitational field, and in other (hypothetical) zero-rest-mass, integer-spin fields coupled to sources in the stars. Paper I analyzed the evolution of scalar-field and gravitational-field perturbations. This paper treats fields of arbitrary integer spin and zero rest mass, using the Newman-Penrose tetrad formalism. The analysis of each multipole ($\mathrm{order}=l$) of each field ($\mathrm{spin}=s$) is reduced to the study of a two-dimensional wave equation, with a curvature potential that differs little from one field to another. The analysis of this wave equation for the scalar case ($s=0$) carries over completely to fields of arbitrary spin $s$. In particular, any radiatable multipole ($l\ensuremath{\ge}s$) gets radiated away completely in the late stages of collapse; if the multipole is static prior to the onset of collapse, it will die out as ${t}^{\ensuremath{-}(2l+2)}$ at late times. Nonradiatable multipoles ($lls$) are conserved. This paper also treats gravitational perturbations in the Newman-Penrose framework, and supplies some technical details missing in the gravitational-perturbation analysis of Paper I.

Consequences of the transversality of the graviton emission amplitude

The divergence condition is used to reconstruct the amplitude for the soft graviton emission in n-particle collisions up to terms linear in graviton momentum q, taking into account terms depending on the spins of the colliding particles. It is shown that the vertex parts for graviton emission are determined uniquely up to the same order in q. In particular, it is proved that no gravitational dipole moments can appear, and it is shown that the existence of dipole moments would contradict the general covariance of the gravitational interaction and the equivalence principle. The cases of colliding particles with spins 0 and 1 2 and of arbitrary integer spin are considered.

Photons and Gravitons inS-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass

We give a purely S-matrix-theoretic proof of the conservation of charge (defined by the strength of soft photon interactions) and the equality of gravitational and inertial mass. Our only assumptions are the Lorentz invariance and pole structure of the S matrix, and the zero mass and spins 1 and 2 of the photon and graviton. We also prove that Lorentz invariance alone requires the S matrix for emission of a massless particle of arbitrary integer spin to satisfy a “mass-shell gauge invariance” condition, and we explain why there are no macroscopic fields corresponding to particles of spin 3 or higher.