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

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases.Comment: 15 pages, two eps files, to appear in Phys. Rev. A 53 (6) (1996

p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency

The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is calculated, and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical phase are noted.Comment: 10 page

Particle production and classical condensates in de Sitter space

The cosmological particle production in a $k=0$ expanding de Sitter universe with a Hubble parameter $H_0$ is considered for various values of mass or conformal coupling of a free, scalar field. One finds that, for a minimally coupled field with mass $0 \leq m^2 < 9 H_0^2/4$ (except for $m^2= 2H_0^2$), the one-mode occupation number grows to unity soon after the physical wavelength of the mode becomes larger than the Hubble radius, and afterwards diverges as $n(t) \sim O(1)(\lambda_{phys}(t)/H_0^{-1})^{2\nu}$, where $\nu \equiv [9/4 - m^2/H_0^2]^{1/2}$. However, for a field with $m^2 > 9H_0^2/4$, the occupation number of a mode outside the Hubble radius is rapidly oscillating and bounded and does not exceed unity. These results, readily generalized for cases of a nonminimal coupling, provide a clear argument that the long-wavelength vacuum fluctuations of low-mass fields in an inflationary universe do show classical behavior, while those of heavy fields do not. The interaction or self-interaction does not appear necessary for the emergence of classical features, which are entirely due to the rapid expansion of the de Sitter background and the upside-down nature of quantum oscillators for modes outside the Hubble radius.Comment: Revtex + 5 postscript figures. Accepted for Phys Rev D15. Revision of Aug 1996 preprint limited to the inclusion and discussion of references suggested by the referee

Deformed oscillator algebras for two dimensional quantum superintegrable systems

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn

The quantum superalgebra Uq[osp(1/2n)]U_q[osp(1/2n)]: deformed para-Bose operators and root of unity representations

We recall the relation between the Lie superalgebra $osp(1/2n)$ and para-Bose operators. The quantum superalgebra $U_q[osp(1/2n)]$, defined as usual in terms of its Chevalley generators, is shown to be isomorphic to an associative algebra generated by so-called pre-oscillator operators satisfying a number of relations. From these relations, and the analogue with the non-deformed case, one can interpret these pre-oscillator operators as deformed para-Bose operators. Some consequences for $U_q[osp(1/2n)]$ (Cartan-Weyl basis, Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra $U_q[gl(n)]$ are pointed out. Finally, using a realization in terms of ``$q$-commuting'' $q$-bosons, we construct an irreducible finite-dimensional unitary Fock representation of $U_q[osp(1/2n)]$ and its decomposition in terms of $U_q[gl(n)]$ representations when $q$ is a root of unity.Comment: 15 pages, LaTeX (latex twice), no figure

Isotopic Grand Unification with the Inclusion of Gravity (revised version)

We introduce a dual lifting of unified gauge theories, the first characterized by the isotopies, which are axiom- preserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincare' symmetry, and the second characterized by the isodualities, which are anti-isomorphic maps with negative-definite generalized units used for the representation of antimatter under the isodualities of the Poincare' symmetry. We then submit, apparently for the first time, a novel grand unification with the inclusion of gravity for matter embedded in the generalized positive-definite units of unified gauge theories while gravity for antimatter is embedded in the isodual isounit. We then show that the proposed grand unification provides realistic possibilities for a resolution of the axiomatic incompatibilities between gravitation and electroweak interactions due to curvature, antimatter and the fundamental space-time symmetries.Comment: 20 pages, Latex, revised in various details and with added reference