A free relativistic anyon with canonical spin algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra {Sμ, Sν} = εμνγSγ. It is shown that it is a general consequence of these features that the Poincaré invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.

The Korteweg-de Vries hierarchy and long water-waves

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.

Anisotropy of crystallite growth during sintering of SnO2 xerogels

The crytallite and pore-size evolution during isothermal sintering (400 ≤ T ≤ 700°C) of SnO2 xerogels was studied by X-ray line broadening and nitrogen adsorption-desorption isotherms. The experimental results show a strong anisotropy of crystallite growth between [110] and [101] directions. The preferential growth at [101] is followed by an increase in the mean pore size, reduction of the specific surface area and invariance of total pore volume. This behaviour is typical of grain coalescence sintering. The kinetic analysis of experimental results suggests that the crystallite coalescence at [101] is governed by lattice diffusion. The strong anisotropy of the growth causes pore-size distribution broadening, hindering the macroscopic shrinkage of the compact during sintering. © 1996 Chapman & Hall.

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.

Manifestly covariant actions for D = 4 self-dual Yang-Mills and D = 10 super-Yang-Mills

Using an infinite number of fields, we construct actions for D = 4 self-dual Yang-Mills with manifest Lorentz invariance and for D = 10 super-Yang-Mills with manifest super-Poincaré invariance. These actions are generalizations of the covariant action for the D = 2 chiral boson which was first studied by McClain, Wu, Yu and Wotzasek.

Torsion and the electromagnetic field

In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.

Off-Diagonal Quark Distributions in Pions in the Effective Single-Instanton Approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables. © 2000 MAIK Nauka/Interperiodica.

Pion-distribution amplitude within the instanton model

The leading-twist pion-distribution amplitude is obtained at a low normalization scale of order ρc (inverse average size of an instanton). Pion dynamics, consistent with gauge invariance and low-energy theorems, is considered within the instanton vacuum model. The results are QCD-evolved to higher momentum-transfer values and are in agreement with recent data from CLEO on the pion transition form factor. It is also shown that some previous calculations violate the axial Ward-Takahashi identity. © 2001 MAIK Nauka/Interperiodica.

Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

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.

Supersymmetric Born-Infeld from the pure spinor formalism of the open superstring

Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N = 1 D = 10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions. © SISSA/ISAS 2003.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Exact time dependent Hopf solitons in 3+1 dimensions

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S2. The construction is based on an ansatz which explores the invariance of the model under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. The model is a rare example of an integrable theory in four dimensions, and the solitons may play a role in the low energy limit of gauge theories. © SISSA 2006.

The temperature dependence of the QCD running coupling

We study the running of the QCD coupling with the momentum squared (Q 2) and the temperature scales in the high temperature limit (T > Tc), using a mass dependent renormalization scheme to build the Renormalization Group Equations. The approach used guaranty gauge invariance, through the use of the Hard Thermal Loop approximation, and independence of the vertex chosen to renormalize the coupling. In general, the dependence of the coupling with the temperature is not logarithmical, although in the region Q2 ∼ T2 the logarithm approximation is reasonable. Finally, as known from Debye screening, color charge is screened in the coupling. The number of flavors, however, is anti-screened.

Analyzing dynamical gluon mass generation

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is presented.