Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein-Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that for spinning particles with nonzero transverse spin components, the torsion induces a precession of particle spin around the direction of the fluid spin. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.Comment: latex, 4 eps figure

Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity

Based on preliminary analysis of the Hamiltonian formulation of the first order Einstein-Cartan action (arXiv:0902.0856 [gr-qc] and arXiv:0907.1553 [gr-qc]) we derive the Darboux coordinates, which are a unique and uniform change of variables preserving equivalence with the original action in all spacetime dimensions higher than two. Considerable simplification of the Hamiltonian formulation using the Darboux coordinates, compared with direct analysis, is explicitly demonstrated. Even an incomplete Hamiltonian analysis in combination with known symmetries of the Einstein-Cartan action and the equivalence of Hamiltonian and Lagrangian formulations allows us to unambiguously conclude that the \textit{unique} \textit{gauge} invariances generated by the first class constraints of the Einstein-Cartan action and the corresponding Hamiltonian are \textit{translation and rotation in the tangent space}. Diffeomorphism invariance, though a manifest invariance of the action, is not generated by the first class constraints of the theory.Comment: 44 pages, references are added, organization of material is slightly modified (additional section is introduced), more details of calculation of the Dirac bracket between translational and rotational constraints are provide

Translational invariance of the Einstein-Cartan action in any dimension

We demonstrate that from the first order formulation of the Einstein-Cartan action it is possible to derive the basic differential identity that leads to translational invariance of the action in the tangent space. The transformations of fields is written explicitly for both the first and second order formulations and the group properties of transformations are studied. This, combined with the preliminary results from the Hamiltonian formulation (arXiv:0907.1553 [gr-qc]), allows us to conclude that without any modification, the Einstein-Cartan action in any dimension higher than two possesses not only rotational invariance but also a form of \textit{translational invariance in the tangent space}. We argue that \textit{not} only a complete Hamiltonian analysis can unambiguously give an answer to the question of what a gauge symmetry is, but also the pure Lagrangian methods allow us to find the same gauge symmetry from the \textit{basic} differential identities.Comment: 25 pages, new Section on group properties of transformations is added, references are added. This version will appear in General Relativity and Gravitatio

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Molecular assessment of complex microbial communities degrading long chain fatty acids in methanogenic bioreactors

Microbial diversity of anaerobic sludge after extended contact with long chain fatty acids (LCFA) was studied using molecular approaches. Samples containing high amounts of accumulated LCFA were obtained after continuous loading of two bioreactors with oleate or with palmitate. These sludge samples were then incubated in batch assays to allow degradation of the biomass-associated LCFA. In addition, sludge used as inoculum for the reactors was also characterized. Predominant phylotypes of the different samples were monitored using denaturing gradient gel electrophoresis (DGGE) of PCR-amplified 16S rRNA gene fragments. Fingerprinting analysis showed changes in bacterial and archaeal communities during LCFA accumulation and degradation. Full-length 16S rRNA gene sequences of 22 clones, representing the predominant bacteria and archaea, were determined. Most bacterial clones (80%) clustered within the Clostridiaceae. Two major groups of methanogens were identified: hydrogen- and formate-utilizing organisms, closely related to Methanobacterium, and acetoclastic organisms closely related to Methanosaeta and Methanosarcina. Quantification by FISH and real-time PCR showed that the relative abundance of archaea increased during degradation of biomass-accumulated LCFA. These results provide insight into the importance and dynamics of balanced communities of bacteria and methanogens in LCFAaccumulation/ degradation cycles.Fundação para a Ciência e a Tecnologia (FCT); Fundo Social Europeu (FSE)

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

Measurement of the CP-Violating Asymmetry Amplitude sin2β\beta

We present results on time-dependent CP-violating asymmetries in neutral B decays to several CP eigenstates. The measurements use a data sample of about 88 million Y(4S) --> B Bbar decays collected between 1999 and 2002 with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We study events in which one neutral B meson is fully reconstructed in a final state containing a charmonium meson and the other B meson is determined to be either a B0 or B0bar from its decay products. The amplitude of the CP-violating asymmetry, which in the Standard Model is proportional to sin2beta, is derived from the decay-time distributions in such events. We measure sin2beta = 0.741 +/- 0.067 (stat) +/- 0.033 (syst) and |lambda| = 0.948 +/- 0.051 (stat) +/- 0.017 (syst). The magnitude of lambda is consistent with unity, in agreement with the Standard Model expectation of no direct CP violation in these modes