Covariant quantization of the superparticle using pure spinors

The ten-dimensional superparticle is covariantly quantized by constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor variable. This same method was recently used for covariantly quantizing the superstring, and it is hoped that the simpler case of the superparticle will be useful for those who want to study this quantization method. It is interesting that quantization of the superparticle action closely resembles quantization of the worldline action for Chern-Simons theory.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.

Covariant quantization of the superstring

After constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor ghost variable, the superstring is covariantly quantized and N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. © 2004 Published by Elsevier B.V.

Consistency between light-front quantization and covariantization for zero modes

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional spurious or unphysical pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory. © World Scientific Publishing Company.

On superfield covariant quantization in general coordinates

We propose a natural extension of the BRST-antiBRST superfield covariant scheme in general coordinates. Thus, the coordinate dependence of the basic tensor fields and scalar density of the formalism is extended from the base supermanifold to the complete set of superfield variables. © Springer-Verlag.

Pseudospin and spin symmetries in the relativistic harmonic oscillator

We compute the analytical solutions of the generalized relativistic harmonic oscillator in 1+1 dimensions, including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs These are the conditions in which pseudospin or spin symmetries can be realized We consider positive and negative quadratic potentials and present their bound-state solutions for fermions and an-tifermions. We relate the spin-type and pseudospin-type spectra through charge conjugation and γ5 chiral transformations. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with tensor interactions and discuss the conditions in which one may have both nucleon and antin-ucleon bound states.

Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result. © 2007 The American Physical Society.

Effect of the Rashba and Dresselhaus spin-splitting terms on the electron g factor in semiconductor quantum wells under applied magnetic fields

We use the Ogg-McCombe Hamiltonian together with the Dresselhaus and Rashba spin-splitting terms to find the g factor of conduction electrons in GaAs-(Ga,Al)As semiconductor quantum wells (QWS) (either symmetric or asymmetric) under a magnetic field applied along the growth direction. The combined effects of non-parabolicity, anisotropy and spin-splitting terms are taken into account. Theoretical results are given as functions of the QW width and compared with available experimental data and previous theoretical works. © 2007 Elsevier B.V. All rights reserved.

Temperature dependence of structural and electronic properties of the spin-liquid candidate κ-(BEDT-TTF) 2Cu 2(CN) 3

We investigate the effect that the temperature dependence of the crystal structure of a two-dimensional organic charge-transfer salt has on the low-energy Hamiltonian representation of the electronic structure. For that, we determine the crystal structure of κ-(BEDT-TTF) 2Cu 2(CN) 3 for a series of temperatures between T=5 and 300 K by single crystal X-ray diffraction and analyze the evolution of the electronic structure with temperature by using density functional theory and tight binding methods. We find a considerable temperature dependence of the corresponding triangular lattice Hubbard Hamiltonian parameters. We conclude that even in the absence of a change of symmetry, the temperature dependence of quantities like frustration and interaction strength can be significant and should be taken into account. © 2012 American Physical Society.

Field-induced length changes in the spin-liquid candidate κ-(BEDT-TTF) 2Cu 2(CN) 3

Measurements of the coefficient of thermal expansion on the spin-liquid candidate κ-(BEDT-TTF) 2Cu 2(CN) 3 have revealed distinct and strongly anisotropic lattice effects around 6 K - a possible spin liquid instability. In order to study the effects of a magnetic field on the low-temperature spin-liquid state, dilatometric measurements have been conducted both as a function of temperature at B = const. and as a function of field at T = const. While the 6 K anomaly is found to be insensitive to magnetic fields B ≤ 10 T, the maximum field applied, surprisingly strong B -induced effects are observed for magnetic fields applied along the in-plane b-axis. Above a threshold field of 0.5 T < B c ≤ 1 T, a jump-like anomaly is observed in the b-axis lattice parameter. This anomaly, which is located at 8.7 K at B = 1 T, grows in size and shifts to lower temperatures with increasing the magnetic field. Although the anomaly bears resemblance to a first-order phase transition, the lack of hysteresis suggests otherwise. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Spin stabilized satellite's attitude propagation with quaternions

This paper presents a study of a modeling scheme for the spin stabilized satellites attitude, entirely developed in terms of quaternion parametrization. The analysis includes numerical propagation of the rotational motion equation, considering the influence of the following torques: aerodynamic, gravity gradient, residual magnetic, eddy currents and the one due to the Lorentz force. Applications are developed considering the Brazilian Spin Stabilized Satellites SCD1 and SCD2, which are quite appropriated for verification and comparison of the theory with the real data generated and processed by the INPE's Satellite Control Center (SCC). The results show that for SCD1 and SCD2 the influence of the eddy current torque is bigger than the others ones, not only due to the orbit altitude, but also to other specific satellites characteristics. The influence of the torque due to Lorentz force is smaller than the others ones because of the dimension and the electrical charges of the SCD1 and SCD2. In all performed tests the errors remained within the dispersion range specified for the attitude determination system of INPE's SCC. The results show the feasibility of using the quaternion attitude parametrization for modeling the satellite dynamics of spin stabilized satellites.

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute.

Search for a narrow, spin-2 resonance decaying to a pair of Z bosons in the qq̄ℓ+ℓ- final state

Results are presented from a search for a narrow, spin-2 resonance decaying into a pair of Z bosons, with one Z-boson decaying into leptons (e+e- or μ+μ-) and the other into jets. An example of such a resonance is the Kaluza-Klein graviton, GKK, predicted in Randall-Sundrum models. The analysis is based on a 4.9 fb-1 sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected with the CMS detector at the LHC. Kinematic and topological properties including decay angular distributions are used to discriminate between signal and background. No evidence for a resonance is observed, and upper limits on the production cross sections times branching fractions are set. In two models that predict Z-boson spin correlations in graviton decays, graviton masses are excluded lower than a value which varies between 610 and 945 GeV, depending on the model and the strength of the graviton couplings. © 2012 CERN.

Spin squeezing and entanglement via finite-dimensional discrete phase-space description

We show how mapping techniques inherent to N2-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson- Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations → entanglement → squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems. © 2013 World Scientific Publishing Company.

Study of the mass and spin-parity of the Higgs boson candidate via its decays to Z boson pairs

A study is presented of the mass and spin-parity of the new boson recently observed at the LHC at a mass near 125 GeV. An integrated luminosity of 17.3 fb-1, collected by the CMS experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, is used. The measured mass in the ZZ channel, where both Z bosons decay to e or μ pairs, is 126.2±0.6(stat) ±0.2(syst) GeV. The angular distributions of the lepton pairs in this channel are sensitive to the spin-parity of the boson. Under the assumption of spin 0, the present data are consistent with the pure scalar hypothesis, while disfavoring the pure pseudoscalar hypothesis. © 2013 CERN. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.