26 research outputs found
Complete set of unitary irreps of Discrete Heisenberg Group
Following the method of induced group representations of Wigner-Mackay, the
explicit construction of all the unitary irreducible representations of the
discrete finite Heisenberg-Weyl group over the discrete phase space
lattice is presented. We explicitly determine
their characters and their fusion rules. We discuss possible physical
applications for finite quantum mechanics and quantum computation.Comment: 25 page
Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map
The aim of this paper is to show that there is a Hopf structure of the
parabosonic and parafermionic algebras and this Hopf structure can generate the
well known Hopf algebraic structure of the Lie algebras, through a realization
of Lie algebras using the parabosonic (and parafermionic) extension of the
Jordan Schwinger map. The differences between the Hopf algebraic and the graded
Hopf superalgebraic structure on the parabosonic algebra are discussed.Comment: 11 pages, LaTex2e fil
Towards laser based improved experimental schemes for multiphoton e+ e- pair production from vacuum
Numerical estimates for pair production from vacuum in the presence of strong
electromagnetic fields are derived, for two experimental schemes : the First
concerns a laser based X-FEL and the other imitates the E144 experiment. The
approximation adopted in this work is that of two level multiphoton on
resonance. Utilizing achievable values of laser beam parameters, an
enhancedproduction efficiency of up to 10^11 and 10^15 pairs can be obtained,
for the two schemes respectively.Comment: 6 pages, 4 figure
On electron-positron pair production using a two level on resonant multiphoton approximation
We present an indepth investigation of certain aspects of the two level on
resonant multiphoton approximation to pair production from vacuum in the
presence of strong electromagnetic fields. Numerical computations strongly
suggest that a viable experimental verification of this approach using modern
optical laser technology can be achieved. It is shown that use of higher
harmonic within the presently available range of laser intensities can lead to
multiphoton processes offering up to 10^12 pairs per laser shot. Finally the
range of applicability of this approximation is examined from the point of view
of admissible values of electric field strength and energy spectrum of the
created pairs.Comment: 10 pages, 5 figure
Generalized boson algebra and its entangled bipartite coherent states
Starting with a given generalized boson algebra U_(h(1)) known as the
bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ
the Hopf duality arguments to provide the dually conjugate function algebra
Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a
closed form expression of the universal T matrix that caps the duality and
generalizes the familiar exponential map relating a Lie algebra with its
corresponding group. Subsequently, using an inverse Mellin transform approach,
the coherent states of single-node systems subject to the U_(h(1)) symmetry
are found to be complete with a positive-definite integration measure.
Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to
generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur
Covariant scalar representation of quantization of the scalar relativistic particle
A covariant scalar representation of is constructed and
analysed in comparison with existing methods for the quantization of the scalar
relativistic particle. It is found that, with appropriately defined
wavefunctions, this produced representation can be identified
with the state space arising from the canonical BFV-BRST quantization of the
modular invariant, unoriented scalar particle (or antiparticle) with admissible
gauge fixing conditions. For this model, the cohomological determination of
physical states can thus be obtained purely from the representation theory of
the algebra.Comment: 16 pages Late
Covariant spinor representation of and quantization of the spinning relativistic particle
A covariant spinor representation of is constructed for the
quantization of the spinning relativistic particle. It is found that, with
appropriately defined wavefunctions, this representation can be identified with
the state space arising from the canonical extended BFV-BRST quantization of
the spinning particle with admissible gauge fixing conditions after a
contraction procedure. For this model, the cohomological determination of
physical states can thus be obtained purely from the representation theory of
the algebra.Comment: Updated version with references included and covariant form of
equation 1. 23 pages, no figure
Coherent and squeezed states of quantum Heisenberg algebras
Starting from deformed quantum Heisenberg Lie algebras some realizations are
given in terms of the usual creation and annihilation operators of the standard
harmonic oscillator. Then the associated algebra eigenstates are computed and
give rise to new classes of deformed coherent and squeezed states. They are
parametrized by deformed algebra parameters and suitable redefinitions of them
as paragrassmann numbers. Some properties of these deformed states also are
analyzed.Comment: 32 pages, 3 figure
On boson algebras as Hopf algebras
Certain types of generalized undeformed and deformed boson algebras which
admit a Hopf algebra structure are introduced, together with their Fock-type
representations and their corresponding -matrices. It is also shown that a
class of generalized Heisenberg algebras including those algebras including
those underlying physical models such as that of Calogero-Sutherland, is
isomorphic with one of the types of boson algebra proposed, and can be
formulated as a Hopf algebra.Comment: LaTex, 18 page