Particles Of Arbitrary Spin Research Articles

A non-Lagrangian approach to gauge symmetry in three dimensions

A non-Lagrangian approach to three-dimensional field theory is discussed. The general classification and construction of Lorentz-covariant, local fields carrying massless and massive particles of arbitrary spin are presented. The ‘‘minimal’’ massive (massless) fields for (half) integer spin are explicitly constructed. Following Weinberg’s analysis in the 4D case it is shown that the gauge symmetry for massive fields results from the group theoretical considerations and the condition that there should exist a long-range interaction.

THE SPINNING CONFORMAL PARTICLE AND ITS BRST QUANTIZATION

We present the classical and quantum theory of the spinning conformal particle. This is a model with manifestly O(2, 4) (conformal) invariance, and it describes both massive and massless particles of arbitrary spin depending on the projection to Minkowski space. We perform both an ordinary BRST quantization and an extended one including the anti-BRST symmetry. It is shown that anti-BRST invariance is necessary to ensure ghost decoupling and make the quantization of the model consistent.

(j, 0) ⊕ (0, j) COVARIANT SPINORS AND CAUSAL PROPAGATORS BASED ON WEINBERG FORMALISM

A pragmatic approach to constructing a covariant phenomenology of the interactions of composite high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin j are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.

G=2 as the natural value of the tree-level gyromagnetic ratio of elementary particles.

We implement at the Lagrangian level a "natural" electromagnetic coupling prescription, different from the minimal one, and proposed a long time ago by Weinberg. This prescription yields, for elementary particles of arbitrary-spin, a gyromagnetic ratio $g=2$ at the tree level. This value is already known to arise in renormalizable theories for spin \textonehalf{} and spin 1, is suggested by the classical, relativistic equations of the spin polarization, and is also found for arbitrary-spin, charged excitations of the open string.

Nonlocal generalized angular-momentum balance laws and equations of motion

It is shown how systems of nonlocal (i.e. integrodifferential) linear second-order equations of motion (LSIDEs) can be directly related to associated nonlocal angular-momentum complexes as well as to balance laws corresponding to such complexes. This gives one the freedom to obtain balance laws from given LSIDEs or vice versa. These laws will, as usual, augment the equations of motion as further useful information about the physical system. Under certain conditions one then sees how the balance laws reduce to corresponding conservation laws. Two examples, sketched to indicate how the formalism can be applied, come from continuum mechanics and quantum mechanics for physical systems described by nonlocal interactions. A third example is from quantum field theory for the case of local interactions for particles of arbitrary integral spin in general, and for electromagnetism in particular. The formalism can thus be appled to physical systems whose equations of motion may be relativistic and either classical or quantum mechanical.

Supersymmetric sum rules on magnetic dipole moments of arbitrary-spin particles

We find model independent, exact sum rules valid for any theory with unbroken N = 1 supersymmetry. These sum rules determine the magnetic dipole moments of all particles within a massive N = 1 supermultiplet in terms of a single free parameter. They imply in particular that, when all magnetic-moment matrix elements are diagonal, the gyromagnetic ratio of arbitrary-spin supersymmetric particles must be equal to 2.

PARADOXICAL KINEMATIC ACAUSALITY IN WEINBERG’S EQUATIONS FOR MASSLESS PARTICLES OF ARBITRARY SPIN

Weinberg’s equations for massless free particles of arbitrary spin are found to have acausal solutions. On the other hand, the m→0 limit of Joos-Weinberg’s finite-mass wave equations satisfied by (j, 0)⊕(0, j) j) covariant spinors are free from all kinematic acausality. This paradoxical situation is resolved and corrected by carefully studying the transition from the classical group theoretical arguments to quantum mechanically interpreted equations.

A BOSONIC MODEL FOR PARTICLES WITH ARBITRARY SPIN

We formulate a simple classical model without Grassmann variables. Quantization of this model gives a unified quantum-mechanical description for massive and massless particles of arbitrary spin and helicity. In the phase space of the classical model a “bosonic” version of the super-Poincaré algebra is realized. At the quantum level it generates the spectrum of the model.

Geometry of spacetime propagation of spinning particles

We develop a unified geometrical description of spacetime propagation of particles of arbitrary spin. We systematize, from the point of view of the theory of induced representations, the various forms of relativistic wave equations. Utilizing Fronsdal's construction of a class of unconstrained wave equations, we obtain closed and explicit forms of the particles' propagators, discuss their analytic properties in the momentum and mass, and express them through subtracted dispersion relations. By requiring unitarity, we then establish the spin-statistics relation. We discuss a class of associative algebras arising in the construction of the propagators and wave functions. These (momentum-space) wave functions are sections of bundles over (complexified) spheres, constructed in analogy to the Yang-Mills instanton bundles. We then derive proper-time and ramdom-walk representations of the propagators. The latter are conveniently expressed in terms of matrix-valued complex “measures” on the spaces of particle's paths. We develop a general method for analyzing fractal properties of sample paths, based on the calculation of ball hitting probabilities (or amplitudes), and find Hausdorff dimensions of paths for half-integer and integer spins.

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.

Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles

Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles

SPIN DEPENDENCE OF THE AHARONOV—BOHM EFFECT

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

Massive and massless Majorana particles of arbitrary spin: Covariant gauge couplings and production properties.

It is shown that massive particles that are their own antiparticles can possess only one specific type of multipolar moments---the so-called toroidal moments. Unlike the familiar charge and magnetic moments, these moments do not directly interact with the (external) static electromagnetic fields but only with the external current, and hence lead to contact interactions. On the other hand, massless Majorana particles, with the exception of those with spin \textonehalf{}, do not have any electromagnetic form factor. It is also found that regardless of the spin of the Majorana particle the differential cross section for the production of a Majorana pair by a spin-1 particle at a high-energy ${e}^{+}{e}^{\ensuremath{-}}$ machine has a unique angular distribution.

NEW MANIFESTLY COVARIANT MODELS FOR RELATIVISTIC PARTICLES OF ARBITRARY SPIN

By means of a previously developed procedure for the derivation of manifestly Lorentz covariant models of spinning particles, we derive new classes of models in which the internal variables transform as Lorentz spinors. Models for massless and massive particles of arbitrary spin are given in which the internal variables are fermionic or bosonic spinors. Lagrangians and their local invariances are explicitly written down for all models.

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF HALF-INTEGER SPIN

We present a program based on BRST techniques for how to obtain the conventional equations for totally symmetric tensor-spinors which describe free massless particles of arbitrary half-integer spin. We do so in a wave function representation in a flat space-time background of any even dimension.

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].

BRST quantization of free massless relativistic particles of arbitrary spin

A BRST quantization of free massless relativistic particles of arbitrary spin is performed. Explicit covariant wave equations are derived for any spin, which are gauge invariant equations. The spinning particles are described by pseudoclassical gauge models in which the spin variables are odd Grassmann numbers. For a spin s particle the gauge group is an O(2 s) extended supersymmetrized reparametrization group. The model has several special features for s⩾1: It cannot be canonically quantized, which makes the solutions to the BRST condition noncanonical. This in turn allows for the peculiarity that there are two equivalent solutions with different ghost numbers.

Stimulated emission of relativistic particles by external sources in spacetime

Explicit solutions are derived for transition amplitudes associated with stimulated emission of relativistic particles by external sources inspacetime. More precisely, exact expressions are obtained for transition amplitudes for any process where there are initially, at a given time, an arbitrary number of particles localized in various regions of space, prior to the switching on of an intervening source, and then, finally, at a later time when the intervening source ceases to operate, a given number of particles are found to be localized in various regions of space. The analysis is given for massive particles ofarbitrary integer and half-integer spins. The solutions are obtained by carrying out a unitarity expansion inconfiguration space, where particles travel between emitters and detectors in the presence of an intervening source. Considered as an application is the process: particle→arbitrary number of particles, where the latter particles emerge spatially with a cone.

Nonlocal conserved quantities, balance laws, and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrodinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.

Complete orthonormal sets on the past light cone. I. Functions belonging to mass zero and helicity s

This is the first of a series of papers preparing the mathematical framework for a past light-cone formulation for the quantum mechanics of particles of arbitrary mass and spin. The aim of past light-cone quantum theory is to define quantum states solely in terms of data accessible to an observer, i.e., information from within his current past light cone. In order to set up such a theory one needs to define on the past light cone complete orthonormal sets of functions that belong to the appropriate unitary irreducible representation of the Poincaré group. Such functions are interpreted as energy-momentum eigenfunctions. The present paper treats the discrete spin, zero mass case for all values of the helicity s=0, 1/2 , (3)/(2) ,. . . .