Related papers: Spinning particles on 2-sphere in accord with the …
Integrable spinning extension of a free particle on 2-sphere is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two…
As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;\alpha)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetric extension of the…
A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or…
A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle.
We consider a model of the classical spinning particle in which the coadjoint orbits of the Poincare group are parametrized by two pairs of canonically conjugate four vectors, one representing the standard position and momentum variables…
Extending our prior investigation, we give a new off-shell construction of theories of spinning particles propagating in Minkowski spaces with arbitrary $N$-extended supersymmetry on the world-line. The basis of the new off-shell…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here, these ideas are generalized to apply to…
An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor…
A universal model for D=4 spinning particle is constructed with the configuration space chosen as ${\bf R}^{3,1}\times S^2$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible…
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…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
Guided by a spinning particle model with U(N)-extended supergravity on the worldline we derive higher spin equations on complex manifolds. Their minimal formulation is in term of gauge fields which satisfy suitable constraints. The latter…
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…
We show that any two left-invariant metrics on $S^3\cong\operatorname{SU}(2)$ which are isospectral for the associated classical Dirac operator $D$ must be isometric. In the case of left-invariant metrics of positive scalar curvature, we…
Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and…