Complete set of unitary irreps of Discrete Heisenberg Group HW2sHW_{2^s}

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 $HW_{2^s}$ over the discrete phase space lattice $Z_{2^s}$ $\otimes$ $Z_{2^s}$ 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 iosp(d,2/2)iosp(d,2/2) quantization of the scalar relativistic particle

A covariant scalar representation of $iosp(d,2/2)$ 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 $iosp(d,2/2)$ 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 $iosp(d,2/2)$ algebra.Comment: 16 pages Late

Covariant spinor representation of iosp(d,2/2)iosp(d,2/2) and quantization of the spinning relativistic particle

A covariant spinor representation of $iosp(d,2/2)$ 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 $iosp(d,2/2)$ 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 $R$-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