A Quantum Anomaly For Rigid Particles

Canonical quantisation of rigid particles is considered paying special attention to the restriction on phase space due to causal propagation. A mixed Lorentz-gravitational anomaly is found in the commutator of Lorentz boosts with world-line reparametrisations. The subspace of gauge invariant physical states is therefore not invariant under Lorentz transformations. The analysis applies for an arbitrary extrinsic curvature dependence with the exception of only one case to be studied separately. Consequences for rigid strings are also discussed.Comment: (replaces previous unpritable version corrupted mailer) 12 pages (Plain TeX), DTP-92/3

Free conical dynamics: charge-monopole as a particle with spin, anyon and nonlinear fermion-monopole supersymmetry

We discuss the origin of the effectively free dynamics of the charge in the magnetic monopole field to apply it for finding the alternative treatment of the charge-monopole as a particle with spin, for tracing out the relation of the charge-monopole to the free relativistic anyon and for clarifying the nature of the non-standard nonlinear supersymmetry of the fermion-monopole system.Comment: 8 pages, to be published in Nuclear Physics B Conference Supplements (D.V.Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', Kharkov, July 25-29, 2000

Zitterbewegung and reduction: 4D spinning particles and 3D anyons on light-like curves

We construct the model with light-like world-lines for the massive 4D spinning particles and 3D anyons. It is obtained via the formal bosonization of pseudoclassical model for the massive Dirac particle with subsequent reduction to the light-like curves. The peculiarity of the light-like trajectories produced due to the Zitterbewegung is explained from the viewpoint of reduction and reparametrization invariance.Comment: 10 pages, discussion expanded and references added. To appear in Phys. Lett.

Nonrelativistic anyons in external electromagnetic field

The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic fields. Consistent coupling of the underlying classical system to arbitrary fields is introduced; at a critical value of the magnetic field, the particle follows a Hall-like law of motion. The corresponding quantized system reveals a hidden nonlocality if the magnetic field is inhomogeneous. In the quantum Landau problem spectral as well as state structure (finite vs. infinite) asymmetry is found. The bound and scattering states, separated by the critical magnetic field phase, behave as further, distinct phases.Comment: 19 pages, typos corrected; to appear in Nucl. Phys.

Symmetries and classical quantization

A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge) and discrete symmetries of the corresponding systems, but there are some special discrete values of them which give rise to the maximal global symmetries at the classical level. Exactly the same values of the parameters are separated at the quantum level, where, in particular, they are singled out by the requirement of conservation of the discrete symmetries. The phenomenon is observed for the familiar pseudoclassical model of 3D P,T-invariant massive fermion system and for a new pseudoclassical model of 3D P,T-invariant system of topologically massive U(1) gauge fields.Comment: 10 pages, LaTe