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Limits on Nonstandard Forces in the Submicrometer Range  [PDF]
M. Masuda,M. Sasaki
Physics , 2009, DOI: 10.1103/PhysRevLett.102.171101
Abstract: We report the search for a nonstandard force by measuring the Casimir forces in the 0.48--6.5 $\mu$m range. By comparing the data and the theory of the Casimir force, we have obtained constraints for the parameter $\alpha$ of the Yukawa-type deviations from Newtonian gravity. The obtained limits are more stringent than previous limits in the 1.0--2.9 $\mu$m range. Furthermore, we have obtained lower limits for the fundamental scale $M_{*}$ for gauged baryon number in the bulk. In particular, for six extra dimensions, the limits on $M_{*}$ are stringent in the range $6.5\times10^{-6}<\rho<2.5\times10^{-4}$.
Contraction and decomposition matrices for vacuum diagrams  [PDF]
K. Knecht,H. Veschelde
Physics , 2001, DOI: 10.1016/S0370-2693(01)01082-6
Abstract: Tensor reduction of vacuum diagrams uses contraction and decomposition matrices. We present general recurrence relations for the calculation of those matrices and an explicit formula for the 3-loop decomposition matrix and its determinant.
On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method  [PDF]
R. Chakrabarti,C. Quesne
Physics , 1998, DOI: 10.1142/S0217751X9900124X
Abstract: The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2)) algebra through a contraction technique. By extending this method, the coloured two-parametric ($h, \alpha$) Jordanian $R_{h,\alpha}^{j_1,z_1;j_2,z_2}$ matrices of the U$_{h,\alpha}$(gl(2)) algebra may be derived from the corresponding coloured $R_{q,\lambda}^{j_1,z_1;j_2,z_2}$ matrices of the standard ($q, \lambda$)-deformed U$_{q,\lambda}$(gl(2)) algebra. Moreover, by using the contraction process as a tool, the coloured $T_{h,\alpha}^{j,z}$ matrices for arbitrary ($j, z$) representations of the Jordanian Fun$_{h,\alpha}$(GL(2)) algebra may be extracted from the corresponding $T_{q,\lambda}^{j,z}$ matrices of the standard Fun$_{q,\lambda}$(GL(2)) algebra.
Vicious walkers and random contraction matrices  [PDF]
Jonathan Novak
Mathematics , 2007,
Abstract: The ensemble $\CUE^{(q)}$ of truncated random unitary matrices is a deformation of the usual Circular Unitary Ensemble depending on a discrete non-negative parameter $q.$ $\CUE^{(q)}$ is an exactly solved model of random contraction matrices originally introduced in the context of scattering theory. In this article, we exhibit a connection between $\CUE^{(q)}$ and Fisher's random-turns vicious walker model from statistical mechanics. In particular, we show that the moment generating function of the trace of a random matrix from $\CUE^{(q)}$ is a generating series for the partition function of Fisher's model, when the walkers are assumed to represent mutually attracting particles.
Two-parameter nonstandard deformation of 2x2 matrices  [PDF]
Salih Celik,Sultan A. Celik
Mathematics , 2001, DOI: 10.1063/1.532907
Abstract: We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup $GL_{p,q}(1|1)$ by a transformation.
Limits of contraction groups and the Tits core  [PDF]
Pierre-Emmanuel Caprace,Colin D. Reid,George A. Willis
Mathematics , 2013,
Abstract: The Tits core G^+ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and if G^+ is non-trivial then it is the unique minimal dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an element the closure of its contraction group is continuous.
Covariant (hh')-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones  [PDF]
C. Quesne
Physics , 1999,
Abstract: $GL_h(n) \times GL_{h'}(m)$-covariant (hh')-bosonic (or (hh')-fermionic) algebras ${\cal A}_{hh'\pm}(n,m)$ are built in terms of the corresponding R_h and $R_{h'}$-matrices by contracting the $GL_q(n) \times GL_{q^{\pm1}}(m)$-covariant q-bosonic (or q-fermionic) algebras ${\cal A}^{(\alpha)}_{q\pm}(n,m)$, $\alpha = 1, 2$. When using a basis of ${\cal A}^{(\alpha)}_{q\pm}(n,m)$ wherein the annihilation operators are contragredient to the creation ones, this contraction procedure can be carried out for any n, m values. When employing instead a basis wherein the annihilation operators, as the creation ones, are irreducible tensor operators with respect to the dual quantum algebra $U_q(gl(n)) \otimes U_{q^{\pm1}}(gl(m))$, a contraction limit only exists for $n, m \in \{1, 2, 4, 6, ...\}$. For n=2, m=1, and n=m=2, the resulting relations can be expressed in terms of coupled (anti)commutators (as in the classical case), by using $U_h(sl(2))$ (instead of sl(2)) Clebsch-Gordan coefficients. Some U_h(sl(2)) rank-1/2 irreducible tensor operators, recently constructed by Aizawa, are shown to provide a realization of ${\cal A}_{h\pm}(2,1)$.
On Nonstandard Quantizations of osp(2|1) Superalgebra via Contraction and Mapping  [PDF]
B. Abdesselam,R. Chakrabarti,A. Hazzab,A. Yanallah
Mathematics , 2003,
Abstract: We develop a generic reprersentation-independent contraction procedure for obtaining, for instance, $R_{\sf h}$ and $L$ operators of arbitrary dimensions for the quantized ${\cal U}_{\sf h}(osp(2|1))$ algebra corresponding to the classical $r_2$ matrix from the pertinent quantities of the standard q-deformed ${\cal U}_q(osp(2|1))$ algebra. Also the quantized ${\bf U_h}(osp(2|1))$ algebra corresponding to the classical $r_1$ matrix comprising of the generators of the classical $sl(2)$ algebra is obtained in terms of a nonlinear basis set.
Nonstandard GL_h(n) quantum groups and contraction of covariant q-bosonic algebras  [PDF]
C. Quesne
Physics , 1998,
Abstract: $GL_h(n) \times GL_h(m)$-covariant $h$-bosonic algebras are built by contracting the $GL_q(n) \times GL_q(m)$-covariant $q$-bosonic algebras considered by the present author some years ago. Their defining relations are written in terms of the corresponding $R_h$-matrices. Whenever $n=2$, and $m=1$ or 2, it is proved by using U_h(sl(2)) Clebsch-Gordan coefficients that they can also be expressed in terms of coupled commutators in a way entirely similar to the classical case. Some U_h(sl(2)) rank-1/2 irreducible tensor operators, recently contructed by Aizawa in terms of standard bosonic operators, are shown to provide a realization of the $h$-bosonic algebra corresponding to $n=2$ and $m=1$.
Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups  [PDF]
Deepak Parashar,Roger J. McDermott
Physics , 1999, DOI: 10.1063/1.533248
Abstract: The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{\lambda,\mu}(2) to yield a new Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide similar realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).
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