A Geometric Model of the Arbitrary Spin Massive Particle

We study some features of bosonic particle path-integral quantization in a twistor-like approach by use of the BRST-BFV quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twistor-like particle by performing a conversion of the Hamiltonian constraints of one formulation to another. A particular feature of the conversion procedure applied to turn the second-class constraints into the first-class constraints is that the simplest Lorentz-covariant way to do this is to convert a full mixed set of the initial first-and second-class constraints rather than explicitly extracting and converting only the second-class constraints. Another novel feature of the conversion procedure applied below is that in the case of the D = 4 and D = 6 twistor-like particle the number of new auxiliary Lorentz-covariant coordinates, which one introduces to get a system of first-class constraints in an extended phase space, exceeds the number of independent second-class constraints of the original dynamical system.We calculate the twistor-like particle propagator in D = 3, 4 and 6 space-time dimensions and show, that it coincides with that of a conventional massless bosonic particle. † on leave from Kharkov Institute of Physics and Technology, Kharkov, 310108, Ukraine.

Section: D=4mentioning

confidence: 99%

On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

Bandos

Maznytsia

Rudychev

et al. 1997

“…The consideration follows the general lines used in Ref. [22] where a similar description has been given for the action of ISO(1, 3) on sphere S 2 . In section 3 we give the Hamilton and Lagrange formulations for the minimal anyon model with the configuration manifold…”

Section: Introductionmentioning

confidence: 99%

“…One can bring Eq. (2.3) to a manifestly covariant form introducing (by analogy with the four-dimensional case [22]) two-component objects z α ≡ (1, z) and z α ≡ ǫ αβ z β = (−z, 1) transforming under (2.3) by the law 4) or in the infinitesimal form…”

Section: Introductionmentioning

confidence: 99%

On the Minimal Model of Anyons

Gorbunov

Kuzenko

Lyakhovich

1997

“…There exists some inherent arbitrariness in the choice of G defined by Eqs. (5) and (6). Such a mapping can be equally well replaced by another one and has the general structure…”

Section: Covariant Realization For the Configuration Spacementioning

confidence: 99%

“…In a recent paper [6], we proposed the model for a massive particle of arbitrary spin in d = 4 Minkowski space R 3,1 as a Poincaré-invariant dynamical system on R 3,1 × S 2 , where S 2 is the space of spin degrees of freedom. The model is based on simple physical and geometrical principles.…”

Section: Introductionmentioning

confidence: 99%

Massive Spinning Particle on Anti-De Sitter Space

Kuzenko

Lyakhovich

Segal

et al. 1996

Self Cite

To describe a massive particle with fixed, but arbitrary, spin on d = 4 anti-de Sitter space M 4 , we propose the point-particle model with configuration space M 6 = M 4 ×S 2 , where the sphere S 2 corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase-space counterparts of the second-and fourth-order Casimir operators for so(3, 2). We prove that the requirement of energy to have a global positive minimum E o over the configuration space is equivalent to the relation E o > s, s being the particle's spin, what presents the classical counterpart of the quantum massive condition. States with the minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on d-dimensional anti-de Sitter space M d , with M 2(d−1) = M d × S (d−2) the corresponding configuration space.