Extra dimensions in superstring theory

It was earlier shown that an SO(9,1) θα spinor variable can be constructed from RNS matter and ghost fields. θα has a bosonic world-sheet super-partner λα which plays the role of a twistor variable, satisfying λΓμ λ = ∂xμ + iθΓμ ∂θ. For Type IIA superstrings, the left-moving [θL α, λL α] and right-moving [θRα, λRα] can be combined into 32-component SO(10,1) spinors [θA, λA]. This suggests that λAΓAB 11 λB = 2λL αλRα can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA superstring and from consideration of DD-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA superstring and an SO(9, 1) × SO(2, 1) structure for the Type IIB superstring. © 1997 Elsevier Science B.V.

Chiral asymmetry and gravitation theory

In this letter we apply an alternative approach, recently developed, to the description of massless particles of arbitrary spin to the case of spin-two particles. This provides a non-geometrical approach to the theory of linearized gravitation. Within this method the chiral components of a spinor field are treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and leads to a formulation that generalizes, to particles of spin-two, the two-component neutrino theory. At the free field level the analog of curvature tensor, spin connection tensor, and metric tensor are independent quantities. By introducing left-right asymmetric linear interactions of these chiral components we get the linearized gravitation theory.

The action for the (propagating) torsion and the limits on the torsion parameters from present experimental data

Starting from the well established form of the Dirac action coupled to the electromagnetic and torsion field we find that there is some additional softly broken local symmetry associated with torsion. This symmetry fixes the form of divergences of the effective action after the spinor fields are integrated out. Then the requirement of renormalizability fixes the torsion field to be equivalent to some massive pseudovector and its action is fixed with accuracy to the values of coupling constant of torsion-spinor interaction, mass of the torsion and higher derivative terms. Implementing this action into the abelian sector of the Standard Model we establish the upper bounds on the torsion mass and coupling. In our study we used results of present experimental limits on four-fermion contact interaction (LEP, HERA, SLAC, SLD, CCFR) and TEVATRON limits on the cross section of new gauge boson, which could be produced as a resonance at high energy pp̄ collisions. © 1998 Elsevier Science B.V. All rights reserved.

Torsion action and its possible observables

The methods of effective field theory are used to explore the theoretical and phenomenological aspects of the torsion field. The spinor action coupled to the electromagnetic field and torsion possesses an additional softly broken gauge symmetry. This symmetry enables one to derive the unique form of the torsion action compatible with unitarity and renormalizability. It turns out that the antisymmetric torsion field is equivalent to a massive axial vector field. The introduction of scalars leads to serious problems which are revealed after the calculation of the leading two-loop divergences. Thus the phenomenological aspects of torsion may be studied only for the fermion-torsion systems. In this part of the paper we obtain upper bounds for the torsion parameters using present experimental data on forward-backward Z-pole asymmetries, data on the experimental limits on four-fermion contact interaction (LEP, HERA, SLAC, SLD, CCFR) and also TEVATRON limits on the cross section of a new gauge boson, which could be produced as a resonance at high energy pp collisions. The present experimental data enable one to put limits on the torsion parameters for the various ranges of the torsion mass. We emphasize that for a torsion mass of the order of the Planck mass no independent theory for torsion is possible, and one must directly use string theory. © 1999 Elsevier Science B.V.

Bose-Einstein condensation for general dispersion relations

Bose-Einstein condensation in an ideal (i.e. interactionless) boson gas can be studied analytically, at university-level statistical and solid state physics, in any positive dimensionality (d > 0) for identical bosons with any positive-exponent (s > 0) energy-momentum (i.e. dispersion) relation. Explicit formulae with arbitrary dls are discussed for: the critical temperature (non-zero only if d/s > 1); the condensate fraction; the internal energy; and the constant-volume specific heat (found to possess a jump discontinuity only if d/s > 2) Classical results are recovered at sufficiently high temperatures. Applications to ordinary' Bose-Einstein condensation, as well as to photons, phonons, ferro-and antiferromagnetic magnons, and (very specially) to Cooper pairs in superconductivity, are mentioned.

Effective action for QED in 2+1 dimensions at finite temperature

Both the parity-breaking and parity-invariant parts of the effective action for the gauge field in QED 3 with massive fermions at finite temperature are obtained exactly. This is feasible because we use a particular configuration of the background gauge field, namely a constant magnetic field and a time-dependent time component of the background gauge field. Our results allow us to compute exactly physically interesting quantities such as the induced charge density and fermion condensate whose dependence on the temperature, fermion mass and gauge field is discussed. ©1999 The American Physical Society.

Squeezed gluon vacuum and the global color model of QCD

We discuss how the vacuum model of Celenza and Shakin with a squeezed gluon condensate can explain the existence of an infrared singular gluon propagator frequently used in calculations within the global color model. In particular, it reproduces a recently proposed QCD-motivated model where low energy chiral parameters were computed as a function of a dynamically generated gluon mass. We show how the strength of the confining interaction of this gluon propagator and the value of the physical gluon condensate may be connected.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

Constraints on space-time manifold in Euclidean supergravity in terms of Dirac eigenvalues

We generalize a previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the space-time manifold, under which space-time admits Dirac eigenvalues as observables, are derived.

Gravitomagnetic moments of the fundamental fields

The quadratic form of the Dirac equation in a Riemann space-time yields a gravitational gyromagnetic ratio κ(S) = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κ(S) = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square-root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS 5 x S 5 is explicitly constructed.

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

Autosolitons in trapped Bose-Einstein condensates with two- and three-body inelastic processes

The conditions for the existence of autosolitons were considered in trapped Bose-Einstein condensates with attractive atomic interactions. The expression for the parameters of the autosoliton was derived using the time-dependent variational approach for the nonconservative 3-dimensional Gross-pitaevskii equation and their stability was checked. The results were in agreement with the exact numerical calculations. It was shown that the transition from unstable to stable point solely depends on the magnitude of the parameters.