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.     

Explicit construction of conserved currents for massless fields of arbitrary spin

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s₁ field and two spin-s₂ fields. The class is restricted only to 2s₂⩽s₁. In case s₁ = 4 and s₂ = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.     

New twistorial integral formulas for massless free fields of arbitrary spin

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields.     

Clustering of Fermi particles with arbitrary spin

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l,s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,..., 2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.     

Free massless fermionic fields of arbitrary spin in d-dimensional anti-de sitter space

Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d−2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.     

Massive lepton-pair production and asymptotically free gauge theories

Logarithmic corrections due to asymptotic freedom are shown to lead to a modified Drell-Yan expression. The production of μ-pairs with high Q_t due to non-Drell-Yan mechanisms is calculated in an asymptotically free non-Abelian gauge theory.     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.     

Production of heavy vector particles in interactions of leptons with the massless gauge bosons

The cross section for vector leptoquark production in electron–gluon collisions is calculated analytically using the Lagrangian with the minimal couplings between the leptoquarks and the gauge fields of the standard model. It is found that the cross section significantly exceeds the corresponding quantity previously presented in the literature. The cross section of exclusive W boson production in neutrino–photon scattering emerges as a by-product of this Letter. The obtained results can be used for studies at ep colliders.     

Covariant polarization density matrix for pure states of particles with integral spin

A closed expression is obtained for the covariant polarization density matrix of pure states of particles with integral spin. The application of the results to the decay f⁰ is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 111–115, August, 1977.I am very grateful to A. B. Govorkov for his interest in the work and valuable comments. I am also very grateful to B. Z. Kopeliovich for a helpful discussion.     

Massive and massless phases in self-dual spin models: Some exact results from the thermodynamic Bethe ansatz

The generally accepted phase diagrams for the discrete spin models in two dimensions imply the existence of certain renormalisation group flows, both between conformal field theories and into a massive phase. Integral equations are proposed to describe these flows, and some properties of their solutions are discussed. The infrared behaviour in massless and massive directions is analysed in detail, and the techniques used are applied to a number of other models.     

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.     

Relativistic polarization density matrix for particles of arbitrary spin

The polarization density matrix for particles of arbitrary spin can be expressed as a linear function of the expectation values of the generators of the polarization symmetry group of the corresponding wave equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–88, April, 1984.     

Confinement of massless particles: Photon

Confinement of massless particles in a suitably chosen dielectric medium is considered. Light waves of selected frequencies are shown to be confined in a medium with dielectric constantε(r)=a/r−b ². A wave theoretical analysis gives equispaced frequency spectrum for the confined light, the radial dependence of its electric wave vector resembling that of hydrogen atom wave functions. In the large frequency limit an eikonal approximation of the problem gives elliptic orbits for the confined rays. Higher frequency orbits are shown to be closer to the centre of the medium than the lower frequency ones.     

General properties of the decay amplitudes for massless particles

We derive the kinematical constraints which characterize the decay of any massless particle in flat space-time. We show that in perturbation theory the decay probabilities of photons and Yang-Mills bosons vanish to all orders and the decay probability of gravitons vanishes to one-loop order for graviton loops and to all orders for matter loops. A general power counting argument indicates in which conditions a decay of a massless particle could be possible: the Lagrangian should contain a self-coupling without derivatives and with a coupling constant of positive mass dimension.