We construct gauge theory of interacting symmetric traceless tensors of all ranks s = 0, 1, 2, 3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d > 2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary hermitian differential operatorĤ, and the symmetric tensors emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around conformally flat pointĤ = 2 with Euclidean metric, the action functional describes conformal higher spin theory. Namely, the linear in fluctuation term cancels, while the one quadratic in fluctuation breaks up as a sum of conformal higher spin theories, the latter being free gauge theories of symmetric traceless tensors of rank s with with the algebra of observables of the quantized point particle. Each global symmetry produces a Noether current constructed out of ψ according to general formula we present in the paper. In the caseĤ = 2 the algebra of observables is an extension of the conformal algebra decomposed w.r.t. its adjoint action as a direct sum of finite-dimensional representations characterized by traceless rectangular two-row Young tableaux. This infinite-dimensional algebra coincides, in d = 3, 4, 6 with conformal higher spin algebras constructed before in terms of even spinor oscillators, which origin is due to twistor reformulation of the dynamics of the massless particle. The construction of the paper may be a starting point for diverse conjectures. First, we discuss the extension of the geometry "quantized point particle + conformal higher spin fields in d dimensions" to the one "tensionless d − 1 brane + higher spin massless fields in d + 1 dimensions", where the phase of ψ appear to describe transverse motion of the brane inside d + 1-bulk. This picture arises in the semiclassical approximation to the quantized particle dynamics, the latter approximation provides d-dimensional generalization of W -geometry elaborated on by Hull in d = 1, 2 case. Next, we propose a candidate on the role of Higgs-like higher spin compensator able to spontaneously break higher spin symmetries. At last, we make the conjecture that, in even dimensions d, the action of conformal higher spin theory equals the logarithmically divergent term of the action of massless higher spin fields on AdS d+1 evaluated on the solutions of Dirichlet-like problem, where conformal higher spin fields are boundary values of massless higher spin fields on AdS d+1 , the latter conjecture conforms with recent proposal (for d = 4) by Tseytlin and provides information on the full higher spin action in AdS d+1 .

A new model of relativistic massive particle with arbitrary spin ((m, s)-particle) is suggested. Configuration space of the model is a product of Minkowski space and two-dimensional sphere, M 6 = R 3,1 × S 2 . The system describes Zitterbewegung at the classical level. Together with explicitly realized Poincaré symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first-class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase-space counterparts of the Casimir operators of the Poincaré group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin-s field. †

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A universal model for D=4 spinning particle is constructed with the configuration space chosen as R 3,1 ×S 2 , where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible world-line first order invariants of the manifold. Each combination of the four constant parameters entering the Lagrangian gives the model, which describes the proper irreducible Poincaré dynamics both at the classical and quantum levels, and thereby the construction uniformly embodies the massive, massless and continuous helicity cases depending upon the special choice of the parameters. For the massive case, the connection with the Souriau approach to elementary systems is established. Constrained Hamiltonian formulation is built and Dirac canonical quantization is performed for the model in the covariant form. An explicit realization is given for the physical wave functions in terms of smooth tensor fields on R 3,1 × S 2 . One-parametric family of consistent interactions with general electromagnetic and gravitational fields is introduced in the massive case. The spin tensor is shown to satisfy the Frenkel-Nyborg equation with arbitrary fixed giromagnetic ratio in a limit of weakly varying electromagnetic field.

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