Two-twistor particle models and free massive higher spin fields

We present D=3 and D=4 models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to the towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor geometry and a second described by a free two-twistor dynamics with constraints. After quantization in the D=3 and D=4 cases, the wave functions are given as functions on the SL(2,R) and SL(2,C) group manifolds respectively, and describe arbitrary on-shell momenta and spin degrees of freedom. Finally, the D=6 case and possible supersymmetric extensions are mentioned.Comment: 37 pages, plain latex, v2. Text in Secs. 1 nd 4 enlarged, references added. Version to appear in JHE

Two-twistor particle models and free massive higher spin fields

Física Teórica, Atómica y Óptic

Master Higher-Spin Particle

We propose a "master" higher-spin (HS) particle system. The particle model relevant to the unfolded formulation of HS theory, as well as the HS particle model with a bosonic counterpart of supersymmetry, follow from the master model as its two different gauges. Quantization of the master system gives rise to a new form of the massless HS equations in an extended space involving, besides extra spinorial coordinates, also a complex scalar one. As solutions to these equations we recover the massless HS multiplet with fields of all integer and half-integer helicities, and obtain new multiplets with a non-zero minimal helicity. The HS multiplets are described by complex wave functions which are holomorphic in the scalar coordinate and carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity as q/2. We construct a twistorial formulation of the master system and present the general solution of the associate HS equations through an unconstrained twistor "prepotential".Comment: 21 pages, minor corrections, version to appear in Class. Quantum Gra

Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields

In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.Comment: 21 pages;v3 more clearly exposed aims and results in the paper; the version which will appear in Journ.Phys.

Galilean Conformal and Superconformal Symmetries

Firstly we discuss briefly three different algebras named as nonrelativistic (NR) conformal: Schroedinger, Galilean conformal and infinite algebra of local NR conformal isometries. Further we shall consider in some detail Galilean conformal algebra (GCA) obtained in the limit c equal to infinity from relativistic conformal algebra O(d+1,2) (d - number of space dimensions). Two different contraction limits providing GCA and some recently considered realizations will be briefly discussed. Finally by considering NR contraction of D=4 superconformal algebra the Galilei conformal superalgebra (GCSA) is obtained, in the formulation using complex Weyl supercharges.Comment: 16 pages, LateX; talk presented at XIV International Conference "Symmetry Methods in Physics", Tsakhkadzor, Armenia, August 16-22, 201

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^{18} = (X_\mu, P_\mu, \eta_\alpha, \oeta_\dalpha, \sigma_\alpha, \osigma_\dalpha, e, \phi), which is derived from the free two-twistor dynamics. The spin sector variables (\eta_\alpha, \oeta_\dalpha, \sigma_\alpha,\ osigma_\dalpha) 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^{18}, derived by a non-linear 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 wavefunction provides a generating functional for free, massive higher spin fields.Comment: FTUV-05-0919, IFIC-05-46, IFT UWr 0110/05. Plain latex file, no macros, 22 pages. A comment and references added. To appear in PRD1

Supertwistors, massive superparticles and k-symmetry

We consider a D=4 two-twistor lagrangian for a massive particle that incorporates the mass-shell condition in an algebraic way, and extend it to a two-supertwistor model with N=2 supersymmetry and central charge identified with the mass. In the purely supertwistorial picture the two D=4 supertwistors are coupled through a Wess-Zumino term in their fermionic sector. We demonstrate how the kappa-gauge symmetry appears in the purely supertwistorial formulation and reduces by half the fermionic degrees of freedom of the two supertwistors; a formulation of the model in terms of kappa-invariant degrees of freedom is also obtained. We show that the kappa-invariant supertwistor coordinates can be obtained by dimensional (D=6 -> D=4) reduction from a D=6 supertwistor. We derive as well by 6 -> 4 reduction the N=2, D=4 massive superparticle model with Wess-Zumino term introduced in 1982. Finally, we comment on general superparticle models constructed with more than two supertwistors.Comment: Shorter version, to appear in JHEP, with emphasis on the D=6 quaternionic structur

Galilean Conformal Mechanics from Nonlinear Realizations

We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a non-relativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one "exotic" central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d non-vanishing space dimensions.Comment: v2: 1 + 20 pages, small changes in Sect.5 and two references added; the version will appear in Phys.Rev.