408 research outputs found
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.
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
Anyon wave equations and the noncommutative plane
The ``Jackiw-Nair'' non-relativistic limit of the relativistic anyon
equations provides us with infinite-component wave equations of the
Dirac-Majorana-Levy-Leblond type for the ``exotic'' particle, associated with
the two-fold central extension of the planar Galilei group. An infinite
dimensional representation of the Galilei group is found. The velocity operator
is studied, and the observable coordinates describing a noncommutative plane
are identified.Comment: 11 pages, typos correcte
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
R-deformed Heisenberg algebra, anyons and d=2+1 supersymmetry
A universal minimal spinor set of linear differential equations describing
anyons and ordinary integer and half-integer spin fields is constructed with
the help of deformed Heisenberg algebra with reflection. The construction is
generalized to some d=2+1 supersymmetric field systems. Quadratic and linear
forms of action functionals are found for the universal minimal as well as for
supersymmetric spinor sets of equations. A possibility of constructing a
universal classical mechanical model for d=2+1 spin systems is discussed.Comment: 11 pages, LaTe
Fractional helicity, Lorentz symmetry breaking, compactification and anyons
We construct the covariant, spinor sets of relativistic wave equations for a
massless field on the basis of the two copies of the R-deformed Heisenberg
algebra. For the finite-dimensional representations of the algebra they give a
universal description of the states with integer and half-integer helicity. The
infinite-dimensional representations correspond formally to the massless states
with fractional (real) helicity. The solutions of the latter type, however,
break down the (3+1) Poincar\'e invariance to the (2+1) Poincar\'e
invariance, and via a compactification on a circle a consistent theory for
massive anyons in =2+1 is produced. A general analysis of the ``helicity
equation'' shows that the (3+1) Poincar\'e group has no massless irreducible
representations with the trivial non-compact part of the little group
constructed on the basis of the infinite-dimensional representations of
sl(2,\CC). This result is in contrast with the massive case where integer and
half-integer spin states can be described on the basis of such representations,
and means, in particular, that the (3+1) Dirac positive energy covariant
equations have no massless limit.Comment: 19 pages; minor changes, references added. To appear in Nucl. Phys.
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.
Deformed Heisenberg algebra and fractional spin field in 2+1 dimensions
With the help of the deformed Heisenberg algebra involving Klein operator, we
construct the minimal set of linear differential equations for the
(2+1)-dimensional relativistic field with arbitrary fractional spin, whose
value is defined by the deformation parameter.Comment: 8 pages, latex file, preprint IC/93/32
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