Massive Higher Spin Fields Research Articles

Massive relativistic particle model with spin from free two-twistor dynamics and its quantization

We consider a relativistic particle model in an enlarged relativistic phase space, M{sup 18}=(X{sub {mu}},P{sub {mu}},{eta}{sub {alpha}},{eta}{sub {alpha}},{sigma}{sub {alpha}},{sigma}{sub {alpha}},e,{phi}), which is derived from the free two-twistor dynamics. The spin sector variables ({eta}{sub {alpha}},{eta}{sub {alpha}},{sigma}{sub {alpha}},{sigma}{sub {alpha}}) satisfy two second class constraints and account for the relativistic spin structure, and the pair (e,{phi}) describes the electric charge sector. After introducing the Liouville one-form on M{sup 18}, derived by a nonlinear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wave function provides a generating functional for free, massive higher spin fields.

The continuous spin limit of higher spin field equations

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity with their product being fixed. The result allows to transform the Wigner equations to a gauge invariant Fronsdal-like form. We also give the generalisation of the Wigner equations to higher dimensions with fields belonging to arbitrary representations of the massless little group.

Massive relativistic particle models with bosonic counterpart of supersymmetry

We consider the massive relativistic particle models on four-dimensional Minkowski space extended by N commuting Weyl spinors for N=1 and N=2. The N=1 model is invariant under the most general form of bosonic counterpart of simple D=4 supersymmetry, and provides after quantization the bosonic counterpart of chiral superfields, satisfying Klein–Gordon equation. In massless case these fields do satisfy the Fierz–Pauli equations. For N=2 we obtain after quantization the free massive higher spin fields for arbitrary spin satisfying linear Bargman–Wigner equations. Finally, the problem of statistics in presented framework for half-integer classical spin fields is discussed.

Massive higher spin fields in (A)dS and in interaction

I outline a series of results obtained in collaboration with A. Waldron on the properties of massive higher (s > 1) spin fields in cosmological, constant curvature, backgrounds and the resulting unexpected quantitative effects on their degrees of freedom and unitarity properties. The dimensional parameter Λ extends the flat space m-line to a (Λ, m) “phase” plane in which these novel phenomena unfold. In this light, I discuss a possible partial resurrection of deSitter supergravity. I will also list the well-known problems of coupling these systems to gravity and, for complex fields, to electromagnetism, systematizing some of the occasionally misunderstood obstacles to interactions, particularly for s = 3/2 and 2.

Inconsistencies of massive charged gravitating higher spins

We examine the causality and degree-of-freedom (DoF) problems encountered by charged, gravitating, massive higher spin fields. For spin s=3/2, making the metric dynamical yields improved causality bounds. These involve only the mass, the product eM P of the charge and Planck mass and the cosmological constant Λ. The bounds are themselves related to a gauge invariance of the timelike component of the field equation at the onset of acausality. While propagation is causal in arbitrary E/M backgrounds, the allowed mass ranges of parameters are of Planck order. Generically, interacting spins s>3/2 are subject to DoF violations as well as to acausality; the former must be overcome before analysis of the latter can even begin. Here we review both difficulties for charged s=2 and show that while a g-factor of 1/2 solves the DoF problem, acausality persists for any g. Separately we establish that no s=2 theory—DoF preserving or otherwise—can be tree unitary.

Massive spinning particles and the geometry of null curves

We study the simplest geometrical particle model associated with null paths in four-dimensional Minkowski space-time. The action is given by the pseudo-arclength of the particle worldline. We show that the reduced classical phase space of this system coincides with that of a massive spinning particle of spin s= α 2/ M, where M is the particle mass, and α is the coupling constant in front of the action. Consistency of the associated quantum theory requires the spin s to be an integer or half integer number, thus implying a quantization condition on the physical mass M of the particle. Then, standard quantization techniques show that the corresponding Hilbert spaces are solution spaces of the standard relativistic massive wave equations. Therefore this geometrical particle model provides us with an unified description of Dirac fermions ( s=1/2) and massive higher spin fields.