Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

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

Cosmological parameters estimation in the Quintessence Paradigm

We present cosmological parameter constraints on flat cosmologies dominated by dark energy using various cosmological data including the recent Archeops angular power spectrum measurements. A likelihood analysis of the existing Cosmic Microwave Background data shows that the presence of dark energy is not requested, in the absence of further prior. This comes from the fact that there exist degeneracies among the various cosmological parameters constrained by the Cosmic Microwave Background. We found that there is a degeneracy in a combination of the Hubble parameter H_0 and of the dark energy equation of state parameter w_Q, but that w_Q is not correlated with the primordial index n of scalar fluctuations and the baryon content Omega_b h^2. Preferred primordial index is n = 0.95 \pm 0.05 (68%) and baryon content Omega_b h^2 = 0.021 \pm 0.003. Adding constraint on the amplitude of matter fluctuations on small scales, sigma_8, obtained from clusters abundance or weak lensing data may allow to break the degenaracies, although present-day systematics uncertainties do not allow firm conclusions yet. The further addition of the Hubble Space Telescope measurements of the local distance scale and of the high redshift supernovae data allows to obtain tight constraints. When these constraints are combined together we find that the amount of dark energy is 0.7^{+0.10}_{-0.07} (95% C.L.) and that its equation of state is very close to those of the vacuum: w_Q 95% C.L.). In no case do we find that quintessence is prefered over the classical cosmological constant, although robust data on sigma_8 might rapidly bring light on this important issue.Comment: 6 pages, 4 figures, submitted to A&

Gravitational lensing in braneworld gravity: formalism and applications

In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We obtain general expressions for measurable quantities such as time delay, deflection angle, Einstein ring and magnification. Subsequently, we estimate the deviations (relative to the standard lensing scenario) in the abovementioned quantities by considering the line elements for clusters and spiral galaxies obtained by solving the effective Einstein equations on the brane. Our analysis reveals that gravitational lensing can be a useful tool for testing braneworld gravity as well as the existence of extra dimensions.Comment: 20 pages, 1 figure, 2 tables. Accepted for publication in Classical and Quantum Gravit

su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions

We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of unitary representations for the su(1, 1) Lie algebra allows us to obtain the energy spectrum and the supersymmetric ground state. For the cases where there exists either scalar or vector potential our results are reduced to those obtained by analytical techniques

Observations of the BL Lac Object 3C 66A with STACEE

We present the analysis and results of recent high-energy gamma-ray observations of the BL Lac object 3C 66A conducted with the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE). During the 2003-2004 observing season, STACEE extensively observed 3C 66A as part of a multiwavelength campaign on the source. A total of 33.7 hours of data was taken on the source, plus an equivalent-duration background observation. After cleaning the data set a total of 16.3 hours of live time remained, and a net on-source excess of 1134 events was seen against a background of 231742 events. At a significance of 2.2 standard deviations this excess is insufficient to claim a detection of 3C 66A, but is used to establish flux upper limits for the source.Comment: Accepted for publication in the Astrophysical Journa

A selected ion flow tube study of the ion-molecule reactions of monochloroethene, trichloroethene and tetrachloroethene

Data for the rate coefficients and product cations of the reactions of a large number of atomic and small molecular cations with monochloroethene, trichloroethene and tetrachloroethene in a selected ion flow tube at 298 K are reported. The recombination energy of the ions range from 6.27 eV (H$_3$O$^+$) through to 21.56 eV (Ne$^+$). Collisional rate coefficients are calculated by modified average dipole orientation theory and compared with experimental values. Thermochemistry and mass balance predict the most feasible neutral products. Together with previously reported results for the three isomers of dichloroethene (J. Phys. Chem. A., 2006, 110, 5760), the fragment ion branching ratios have been compared with those from threshold photoelectron photoion coincidence spectroscopy over the photon energy range 9-22 eV to determine the importance or otherwise of long-range charge transfer. For ions with recombination energy in excess of the ionisation energy of the chloroethene, charge transfer is energetically allowed. The similarity of the branching ratios from the two experiments suggest that long-range charge transfer is dominant. For ions with recombination energy less than the ionisation energy, charge transfer is not allowed; chemical reaction can only occur following formation of an ion-molecule complex, where steric effects are more significant. The products that are now formed and their percentage yield is a complex interplay between the number and position of the chlorine atoms with respect to the C=C bond, where inductive and conjugation effects can be important