ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Cytochrome c′ folding triggered by electron transfer: Fast and slow formation of four-helix bundles

Reduced (FeII) Rhodopseudomonas palustris cytochrome c′ (Cyt c′) is more stable toward unfolding ([GuHCl]1/2 = 2.9(1) M) than the oxidized (FeIII) protein ([GuHCl]1/2 = 1.9(1) M). The difference in folding free energies (ΔΔGf° = 70 meV) is less than half of the difference in reduction potentials of the folded protein (100 mV vs. NHE) and a free heme in aqueous solution (≈−150 mV). The spectroscopic features of unfolded FeII–Cyt c′ indicate a low-spin heme that is axially coordinated to methionine sulfur (Met-15 or Met-25). Time-resolved absorption measurements after CO photodissociation from unfolded FeII(CO)–Cyt c′ confirm that methionine can bind to the ferroheme on the microsecond time scale [kobs = 5(2) × 104 s−1]. Protein folding was initiated by photoreduction (two-photon laser excitation of NADH) of unfolded FeIII–Cyt c′ ([GuHCl] = 2.02–2.54 M). Folding kinetics monitored by heme absorption span a wide time range and are highly heterogeneous; there are fast-folding (≈103 s−1), intermediate-folding (102–101 s−1), and slow-folding (10−1 s−1) populations, with the last two likely containing methionine-ligated (Met-15 or Met-25) ferrohemes. Kinetics after photoreduction of unfolded FeIII–Cyt c′ in the presence of CO are attributable to CO binding [1.4(6) × 103 s−1] and FeII(CO)–Cyt c′ folding [2.8(9) s−1] processes; stopped-flow triggered folding of FeIII–Cyt c′ (which does not contain a protein-derived sixth ligand) is adequately described by a single kinetics phase with an estimated folding time constant of ≈4 ms [ΔGf° = −33(3) kJ mol−1] at zero denaturant.

Extreme Harmonic Generation In Electrically Driven Spin Resonance.

We report the observation of multiple harmonic generation in electric dipole spin resonance in an InAs nanowire double quantum dot. The harmonics display a remarkable detuning dependence: near the interdot charge transition as many as eight harmonics are observed, while at large detunings we only observe the fundamental spin resonance condition. The detuning dependence indicates that the observed harmonics may be due to Landau-Zener transition dynamics at anticrossings in the energy level spectrum.

Measurement Of Longitudinal Spin Asymmetries For Weak Boson Production In Polarized Proton-proton Collisions At Rhic.

We report measurements of single- and double-spin asymmetries for W^{±} and Z/γ^{*} boson production in longitudinally polarized p+p collisions at sqrt[s]=510  GeV by the STAR experiment at RHIC. The asymmetries for W^{±} were measured as a function of the decay lepton pseudorapidity, which provides a theoretically clean probe of the proton's polarized quark distributions at the scale of the W mass. The results are compared to theoretical predictions, constrained by polarized deep inelastic scattering measurements, and show a preference for a sizable, positive up antiquark polarization in the range 0.05

Site Specific Spin Dynamics In Bafe2as2: Tuning The Ground State By Orbital Differentiation.

The role of orbital differentiation on the emergence of superconductivity in the Fe-based superconductors remains an open question to the scientific community. In this investigation, we employ a suitable microscopic spin probe technique, namely Electron Spin Resonance (ESR), to investigate this issue on selected chemically substituted BaFe2As2 single crystals. As the spin-density wave (SDW) phase is suppressed, we observe a clear increase of the Fe 3d bands anisotropy along with their localization at the FeAs plane. Such an increase of the planar orbital content is interestingly independent of the chemical substitution responsible for suppressing the SDW phase. As a consequence, the magnetic fluctuations in combination with this particular symmetry of the Fe 3d bands are propitious ingredients for the emergence of superconductivity in this class of materials.

Anomalous thermodynamic properties in ferropericlase throughout its spin crossover transition

The thermodynamics properties of ferropericlase (Mg(1-x)Fe(x)O where x=0.1875) (Fp) throughout its spin crossover were investigated by first principles. Fp was treated as an ideal solid solution of pure high-spin and low-spin states. The Gibbs free energies of the pure states were addressed using the LDA+U method. A vibrational virtual-crystal model was developed to address the vibrational properties of the pure spin cases and used in conjunction with quasiharmonic theory to compute their vibrational free energies. The thermodynamics properties of Fp display significant anomalies that should be typical of spin crossover systems in general. In Fp, in particular, they are fundamental for understanding the state of earth's interior, where the pressure and temperature conditions of the crossover are realized.

Forward Neutral-Pion Transverse Single-Spin Asymmetries in p plus p Collisions at s=200 GeV

We report precision measurements of the Feynman x (x(F)) dependence, and first measurements of the transverse momentum (p(T)) dependence, of transverse single-spin asymmetries for the production of pi(0) mesons from polarized proton collisions at s=200 GeV. The x(F) dependence of the results is in fair agreement with perturbative QCD model calculations that identify orbital motion of quarks and gluons within the proton as the origin of the spin effects. Results for the p(T) dependence at fixed x(F) are not consistent with these same perturbative QCD-based calculations.

Longitudinal double-spin asymmetry for inclusive jet production in (p)over-right-arrow + (p)over-right-arrow collisions at root s=200 GeV

We report a new STAR measurement of the longitudinal double-spin asymmetry A(LL) for inclusive jet production at midrapidity in polarized p+p collisions at a center-of-mass energy of root s = 200 GeV. The data, which cover jet transverse momenta 5 < p(T) < 30 GeV/c, are substantially more precise than previous measurements. They provide significant new constraints on the gluon spin contribution to the nucleon spin through the comparison to predictions derived from one global fit to polarized deep-inelastic scattering measurements. They provide significant new constraints on the gluon spin contribution to the nucleon spin through the comparison to predictions derived from one global fit to polarized deep-inelastic scattering measurements.

Spin alignment measurements of the K*(0)(892) and phi(1020) vector mesons in heavy ion collisions at root S(NN)=200 GeV

We present the first spin alignment measurements for the K*(0)(892) and phi(1020) vector mesons produced at midrapidity with transverse momenta up to 5 GeV/c at root s(NN) = 200 GeV at RHIC. The diagonal spin-density matrix elements with respect to the reaction plane in Au+Au collisions are rho(00) = 0.32 +/- 0.04 (stat) +/- 0.09 (syst) for the K*(0) (0.8 < p(T) < 5.0 GeV/c) and rho(00) = 0.34 +/- 0.02 (stat) +/- 0.03 (syst) for the phi (0.4 < p(T) < 5.0 GeV/c) and are constant with transverse momentum and collision centrality. The data are consistent with the unpolarized expectation of 1/3 and thus no evidence is found for the transfer of the orbital angular momentum of the colliding system to the vector-meson spins. Spin alignments for K(*0) and phi in Au+Au collisions were also measured with respect to the particle's production plane. The phi result, rho(00) = 0.41 +/- 0.02 (stat) +/- 0.04 (syst), is consistent with that in p+p collisions, rho(00) = 0.39 +/- 0.03 (stat) +/- 0.06 (syst), also measured in this work. The measurements thus constrain the possible size of polarization phenomena in the production dynamics of vector mesons.

Resummation of infrared divergences in the free energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing noninteracting spin-two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

Cross Section and Parity-Violating Spin Asymmetries of W(+/-) Boson Production in Polarized p plus p Collisions at root s=500 Gev

Large parity-violating longitudinal single-spin asymmetries A(L)(e+) = 0.86(-0.14)(+0.30) and Ae(L)(e-) = 0.88(-0.71)(+0.12) are observed for inclusive high transverse momentum electrons and positrons in polarized p + p collisions at a center-of-mass energy of root s = 500 GeV with the PHENIX detector at RHIC. These e(+/-) come mainly from the decay of W(+/-) and Z(0) bosons, and their asymmetries directly demonstrate parity violation in the couplings of the W(+/-) to the light quarks. The observed electron and positron yields were used to estimate W(+/-) boson production cross sections for the e(+/-) channels of sigma(pp -> W(+)X) X BR(W(+) -> e(+) nu(e)) = 144.1 +/- 21.2(stat)(-10.3)(+3.4)(syst) +/- 21.6(norm) pb, and sigma(pp -> W(-)X) X BR(W(-) -> e(-) (nu) over bar (e)) = 3.17 +/- 12.1(stat)(-8.2)(+10.1)(syst) +/- 4.8(norm) pb.

Measurement of transverse single-spin asymmetries for J/psi production in polarized p plus p collisions at root s=200 GeV

We report the first measurement of transverse single-spin asymmetries in J/psi production from transversely polarized p + p collisions at root s = 200 GeV with data taken by the PHENIX experiment in 2006 and 2008. The measurement was performed over the rapidity ranges 1.2 < vertical bar y vertical bar < 2.2 and vertical bar y vertical bar < 0.35 for transverse momenta up to 6 GeV/c. J/psi production at the Relativistic Heavy Ion Collider is dominated by processes involving initial-state gluons, and transverse single-spin asymmetries of the J/psi can provide access to gluon dynamics within the nucleon. Such asymmetries may also shed light on the long-standing question in QCD of the J/psi production mechanism. Asymmetries were obtained as a function of J/psi transverse momentum and Feynman-x, with a value of -0.086 +/- 0.026(stat) +/- 0.003(syst) in the forward region. This result suggests possible nonzero trigluon correlation functions in transversely polarized protons and, if well defined in this reaction, a nonzero gluon Sivers distribution function.

Gluon-Spin Contribution to the Proton Spin from the Double-Helicity Asymmetry in Inclusive pi(0) Production in Polarized p plus p Collisions at root s=200 GeV

The double helicity asymmetry in neutral pion production for p(T) = 1 to 12 GeV/c was measured with the PHENIX experiment to access the gluon-spin contribution, Delta G, to the proton spin. Measured asymmetries are consistent with zero, and at a theory scale of mu 2 = 4 GeV(2) a next to leading order QCD analysis gives Delta G([0.02,0.3]) = 0.2, with a constraint of -0.7 < Delta G([0.02,0.3]) < 0.5 at Delta chi(2) = 9 (similar to 3 sigma) for the sampled gluon momentum fraction (x) range, 0.02 to 0.3. The results are obtained using predictions for the measured asymmetries generated from four representative fits to polarized deep inelastic scattering data. We also consider the dependence of the Delta G constraint on the choice of the theoretical scale, a dominant uncertainty in these predictions.

Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of the spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spatial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external electromagnetic field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, Delta x Delta y >= theta(2)/2, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.