Differential Calculus on the Quantum Superspace and Deformation of Phase Space

We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum deformation of the general linear supergroup, $GL_q(m|n)$, is studied and the explicit form for the ${\hat R}$-matrix, which is the solution of the Yang-Baxter equation, is presented. We derive the quantum-matrix commutation relation of $GL_q(m|n)$ and the quantum superdeterminant. We apply these results for the $GL_q(m|n)$ to the deformed phase-space of supercoordinates and their momenta, from which we construct the ${\hat R}$-matrix of q-deformed orthosymplectic group $OSp_q(2n|2m)$ and calculate its ${\hat R}$-matrix. Some detailed argument for quantum super-Clifford algebras and the explict expression of the ${\hat R}$-matrix will be presented for the case of $OSp_q(2|2)$.Comment: 17 pages, KUCP-4

Minimal deformations of the commutative algebra and the linear group GL(n)

We consider the relations of generalized commutativity in the algebra of formal series $M_q (x^i )$, which conserve a tensor $I_q$-grading and depend on parameters $q(i,k)$ . We choose the $I_q$-preserving version of differential calculus on $M_q$ . A new construction of the symmetrized tensor product for $M_q$-type algebras and the corresponding definition of minimally deformed linear group $QGL(n)$ and Lie algebra $qgl(n)$ are proposed. We study the connection of $QGL(n)$ and $qgl(n)$ with the special matrix algebra \mbox{Mat} (n,Q) containing matrices with noncommutative elements. A definition of the deformed determinant in the algebra \mbox{Mat} (n,Q) is given. The exponential parametrization in the algebra \mbox{Mat} (n,Q) is considered on the basis of Campbell-Hausdorf formula.Comment: 14 page

Representations of the quantum matrix algebra Mq,p(2)M_{q,p}(2)

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $M_{ q,p}(2)$ ( the coordinate ring of $GL_{q,p}(2)$) exist only when both q and p are roots of unity. In this case th e space of states has either the topology of a torus or a cylinder which may be thought of as generalizations of cyclic representations.Comment: 20 page

Quantum Deformed su(m∣n)su(m|n) Algebra and Superconformal Algebra on Quantum Superspace

We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed $su(1|4)$ algebra, we derive deformed Lorentz, translation of Minkowski space, $iso(2,2)$ and its supersymmetric algebras as closed subalgebras with consistent automorphisms.Comment: 27 pages, KUCP-59, LaTeX fil

Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces

Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they have the same dimensions as in the classical case. Formal solutions of the corresponding Klein--Gordon and Dirac equations are found. The Fock space construction is sketched.Comment: 21 pages, LaTeX file, minor change

Lagrangian and Hamiltonian Formalism on a Quantum Plane

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on $TQ_{q,p}$. These two differential calculi can in principle give rise to two different particle dynamics, starting from a single Lagrangian. For Hamiltonian mechanics, we define a phase space $T^*Q_{q,p}$ spanned by noncommuting particle coordinates and momenta. The commutation relations for the momenta can be determined only after knowing their functional dependence on coordinates and velocities. Thus these commutation relations, as well as the differential calculus on $T^*Q_{q,p}$, depend on the initial choice of Lagrangian. We obtain the deformed Hamilton's equations of motion and the deformed Poisson brackets, and their definitions also depend on our initial choice of Lagrangian. We illustrate these ideas for two sample Lagrangians. The first system we examine corresponds to that of a nonrelativistic particle in a scalar potential. The other Lagrangian we consider is first order in time derivative

THE EXPRESSION OF H-2K, H-2D AND Ia ANTIGENS IN VARIOUS TISSUES AS ASSESSED IN Fc RECEPTOR INHIBITION SYSTEMS

The ability of mouse alloantibody to inhibit EA rosette formation and antibody-dependent cell-mediated cytotoxicity (ADCC) was used to study the expression of H-2K, Ia and H-2D antigens in various tissues. As previously reported antisera against each of these groups of antigens inhibited B lymphocyte EA rosette formation. Continuing studies confirmed these observations but established that quantitative differences may exist in the ease with which antibody against antigens in each region can inhibit EA rosettes: anti H-2D and anti-Ia seemed stronger relative to their cytotoxic titres than anti H-2K. Possible reasons for this are discussed. When rosette forming cells from other tissues were studied, (bone marrow cells, peritoneal macrophages and tumour cells), they were inhibited by anti H-2K and anti H-2D sera but not by anti Ia sera, presumably reflecting the restricted distribution of Ia antigens in those tissues. Inhibition of ADCC by various antisera reflected qualitatively and quantitatively the expression of H-2 antigens in various tissues: whereas effector cell activity in spleen, bone marrow, or peritoneal cell populations was inhibited by anti H-2 or anti-Ia sera, the amount of inhibition observed with anti-Ia was much less when the tissue expressed little Ia antigen (bone marrow) than when it expressed abundant Ia antigen (spleen). The ability of cytotoxicity inhibition to detect antibody coated cells was used to assess the relative amount of Ia antigen on thymus and on lymph node cells, showing significant amounts of Ia antigen on thymus cells. Fc receptor inhibition studies may thus be useful as new approaches to the study of the expression of the antigens of the major histocompatibility complex.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74647/1/j.1744-313X.1975.tb00547.x.pd

Too little radiation pressure on dust in the winds of oxygen-rich AGB stars

New dynamical models for dust-driven winds of oxygen-rich AGB stars are presented which include frequency-dependent Monte Carlo radiative transfer by means of a sparse opacity distribution technique and a time-dependent treatment of the nucleation, growth and evaporation of inhomogeneous dust grains composed of a mixture of Mg2SiO4, SiO2, Al2O3, TiO2, and solid Fe. The frequency-dependent treatment of radiative transfer reveals that the gas is cold close to the star (700-900 K at 1.5-2 R*) which facilitates the nucleation process. The dust temperatures are strongly material-dependent, with differences as large as 1000 K for different pure materials, which has an important influence on the dust formation sequence. Two dust layers are formed in the dynamical models: almost pure glassy Al2O3 close to the star (r > 1.5 R*) and the more opaque Fe-poor Mg-Fe-silicates further out. Solid Fe or Fe-rich silicates are found to be the only condensates that can efficiently absorb the stellar light in the near IR. Consequently, they play a crucial role for the wind driving mechanism and act as thermostat. Only small amounts of Fe can be incorporated into the grains, because otherwise the grains get too hot. Thus, the models reveal almost no mass loss, and no dust shells.Comment: 4 pages, 3 figures. accepted as A&A letter after minor revision

On the Differential Geometry of GLq(1∣1)GL_q(1| 1)

The differential calculus on the quantum supergroup GL$_q(1| 1)$ was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL$_q(1| 1)$ in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix $\hat{R}$Comment: 14 page