Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.Comment: 23 pages, 2 table

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

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

Transport of Anthocyanins and other Flavonoids by the Arabidopsis ATP-Binding Cassette Transporter AtABCC2

Flavonoids have important developmental, physiological, and ecological roles in plants and are primarily stored in the large central vacuole. Here we show that both an ATP-binding cassette (ABC) transporter(s) and an H+-antiporter(s) are involved in the uptake of cyanidin 3-O-glucoside (C3G) by Arabidopsis vacuolar membrane-enriched vesicles. We also demonstrate that vesicles isolated from yeast expressing the ABC protein AtABCC2 are capable of MgATP-dependent uptake of C3G and other anthocyanins. The uptake of C3G by AtABCC2 depended on the co-transport of glutathione (GSH). C3G was not altered during transport and a GSH conjugate was not formed. Vesicles from yeast expressing AtABCC2 also transported flavone and flavonol glucosides. We performed ligand docking studies to a homology model of AtABCC2 and probed the putative binding sites of C3G and GSH through site-directed mutagenesis and functional studies. These studies identified residues important for substrate recognition and transport activity in AtABCC2, and suggest that C3G and GSH bind closely, mutually enhancing each other’s binding. In conclusion, we suggest that AtABCC2 along with possibly other ABCC proteins are involved in the vacuolar transport of anthocyanins and other flavonoids in the vegetative tissue of Arabidopsis

Gauging the spacetime metric -- looking back and forth a century later

H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field theory of electromagnetism and gravity. After getting disillusioned with this research program and after the rise of a convincing alternative for the gauge idea by translating it to the phase of wave functions and spinor fields in quantum mechanics, Weyl no longer considered the original scale gauge as physically relevant. About the middle of the last century the question of conformal and/or local scale gauge transformation were reconsidered by different authors in high energy physics (Bopp, Wess, et al.) and, independently, in gravitation theory (Jordan, Fierz, Brans, Dicke). In this context Weyl geometry attracted new interest among different groups of physicists (Omote/Utiyama/Kugo, Dirac/Canuto/Maeder, Ehlers/Pirani/Schild and others), often by hypothesizing a new scalar field linked to gravity and/or high energy physics. Although not crowned by immediate success, this ``retake'' of Weyl geometrical methods lives on and has been extended a century after Weyl's first proposal of his basic geometrical structure. It finds new interest in present day studies of elementary particle physics, cosmology, and philosophy of physics.Comment: 56 pages, contribution to Workshop Hundred Years of Gauge Theory Bad Honnef, July 30 - August 3, 201

Educação Física Escolar: Percepções do Aluno com Deficiência1

RESUMO: a inclusão de alunos com deficiência é prevista em lei e manter boas estruturas físicas e pedagógicas na escola é um ponto fundamental para que o acesso possa acontecer. A Educação Física faz parte desta inclusão e pode proporcionar grandes melhoras na qualidade de vida de alunos com deficiência. Este estudo teve como objetivo compreender as percepções do aluno com deficiência a respeito das aulas de Educação Física. Para isso foi realizada uma pesquisa de natureza qualitativa utilizando para coleta de dados uma entrevista semiestruturada a qual foi gravada, transcrita e posteriormente analisada. A amostra foi constituída de 20 alunos com deficiência matriculados em escolas regulares da cidade de Santos Dumont - MG. A partir das entrevistas, destacou-se a percepção do aluno com deficiência a respeito da Educação Física escolar; o entendimento deles quanto ao conceito de qualidade de vida; as melhoras proporcionadas na qualidade de vida através da Educação Física; as facilidades e as dificuldades nas aulas; e as questões concernentes à relação aluno/professor e aluno/aluno. Os resultados dessa pesquisa podem auxiliar a comunidade escolar e o professor de Educação Física a melhorarem a inclusão nas escolas regulares. Além disso, as percepções dos alunos com deficiência sobre as aulas podem ajudar o professor na busca de um ambiente melhor com aulas que atendam a todos e proporcionem uma melhor qualidade de vida