17 research outputs found
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp(1|2) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator
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.
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.
Superconformal mechanics and nonlinear supersymmetry
We show that a simple change of the classical boson-fermion coupling
constant, , , in the superconformal mechanics
model gives rise to a radical change of a symmetry: the modified classical and
quantum systems are characterized by the nonlinear superconformal symmetry. It
is generated by the four bosonic integrals which form the so(1,2) x u(1)
subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2
so(1,2)-representations and anticommuting for the order n polynomials of the
even generators. We find that the modified quantum system with an integer value
of the parameter is described simultaneously by the two nonlinear
superconformal symmetries of the orders relatively shifted in odd number. For
the original quantum model with , , this means the
presence of the order 2p nonlinear superconformal symmetry in addition to the
osp(2|2) supersymmetry.Comment: 16 pages; misprints corrected, note and ref added, to appear in JHE
De Sitter Cosmic Strings and Supersymmetry
We study massive spinor fields in the geometry of a straight cosmic string in
a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic
solutions of the equations of motion. We connect the zero mode solutions to the
heat-kernel regularized Witten index of the supersymmetric algebra.Comment: Version similar to the one accepted by General Relativity and
Gravitatio
Higher Spins from Tensorial Charges and OSp(N|2n) Symmetry
It is shown that the quantization of a superparticle propagating in an N=1,
D=4 superspace extended with tensorial coordinates results in an infinite tower
of massless spin states satisfying the Vasiliev unfolded equations for free
higher spin fields in flat and AdS_4 N=1 superspace. The tensorial extension of
the AdS_4 superspace is proved to be a supergroup manifold OSp(1|4). The model
is manifestly invariant under an OSp(N|8) (N=1,2) superconformal symmetry. As a
byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n)
groups are GL(2n) flat, i.e. they are equivalent to flat Cartan forms up to a
GL(2n) rotation. This property is crucial for carrying out the quantization of
the particle model on OSp(1|4) and getting the higher spin field dynamics in
super AdS_4, which can be performed in a way analogous to the flat case.Comment: LaTeX, 21 page (JHEP style), misprints corrected, added comments on
the relation of results of hep-th/0106149 with hep-th/9904109 and
hep-th/9907113, references adde
Rigid Rotor as a Toy Model for Hodge Theory
We apply the superfield approach to the toy model of a rigid rotor and show
the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, under
which, the kinetic term and action remain invariant. Furthermore, we also
derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST
symmetry transformations, under which, the gauge-fixing term and Lagrangian
remain invariant. The anticommutator of the above nilpotent symmetry
transformations leads to the derivation of a bosonic symmetry transformation,
under which, the ghost terms and action remain invariant. Together, the above
transformations (and their corresponding generators) respect an algebra that
turns out to be a physical realization of the algebra obeyed by the de Rham
cohomological operators of differential geometry. Thus, our present model is a
toy model for the Hodge theory.Comment: LaTeX file, 22 page
Regularizing Property of the Maximal Acceleration Principle in Quantum Field Theory
It is shown that the introduction of an upper limit to the proper
acceleration of a particle can smooth the problem of ultraviolet divergencies
in local quantum field theory. For this aim, the classical model of a
relativistic particle with maximal proper acceleration is quantized canonically
by making use of the generalized Hamiltonian formalism developed by Dirac. The
equations for the wave function are treated as the dynamical equations for the
corresponding quantum field. Using the Green's function connected to these wave
equations as propagators in the Feynman integrals leads to an essential
improvement of their convergence properties.Comment: 9 pages, REVTeX, no figures, no table
Heisenberg-type structures of one-dimensional quantum Hamiltonians
We construct a Heisenberg-like algebra for the one dimensional infinite
square-well potential in quantum mechanics. The ladder operators are realized
in terms of physical operators of the system as in the harmonic oscillator
algebra. These physical operators are obtained with the help of variables used
in a recently developed non commutative differential calculus. This
\textquotedblleft square-well algebra\textquotedblright is an example of an
algebra in a large class of generalized Heisenberg algebras recently
constructed. This class of algebras also contains -oscillators as a
particular case. We also discuss the physical content of this large class of
algebras.Comment: 11 pages. The title and abstract were modified and minor corrections
were made in the paper's core. Final version to appear in Phys. Rev.
Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach
We investigate variations of the Zitterbewegung frequency of electron due to
an external static and uniform magnetic field employing the expectation value
quantum approach, and compare our results with the classical model of spinning
particles. We demonstrate that these two so far compatible approaches are not
in agreement in the presence of an external uniform static magnetic field, in
which the classical approach breaks the usual symmetry of free particles and
antiparticles states, i.e. it leads to CP violation. Hence, regarding the
Zitterbewegung frequency of electron, the classical approach in the presence of
an external magnetic field is unlikely to correctly describe the spin of
electron, while the quantum approach does, as expected. We also show that the
results obtained via the expectation value are in close agreement with the
quantum approach of the Heisenberg picture derived in the literature. However,
the method we use is capable of being compared with the classical approach
regarding the spin aspects. The classical interpretation of spin produced by
the altered Zitterbewegung frequency, in the presence of an external magnetic
field, are discussed.Comment: 16 pages, no figure