Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

MAPPING CORRELATION-FUNCTIONS OF SCHWINGER AND AXIAL MODELS

We show that all Green's functions of the Schwinger and axial models can be obtained one from the other. In particular, we show that the two models have the same chiral anomaly. Finally it is demonstrated that the Schwinger model can keep gauge invariance for an arbitrary mass, dispensing with an additional gauge group integration.

New possibilities for the gauging of chiral bosons

We study a new mechanism for the electromagnetic gauging of chiral bosons showing that new possibilities emerge for the interacting theory of chiral scalars. We introduce a chirally coupled gauge field necessary to mod out the degree of freedom that obstructs gauge invariance in a system of two opposite chiral bosons soldering them together.

SUPERSYMMETRIC CONSTRUCTION OF W-ALGEBRAS FROM SUPER TODA AND WZNW THEORIES

A systematic construction of super W algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy momentum tensor, is discussed in general terms for all super Lie algebras whose simple roots are fermionic. A detailed discussion employing the Dirac bracket structure and an explicit construction of W algebras for the cases of OSP(1, 2), OSP(2, 2), OSP(3, 2) and D(2, 1\ alpha) are given. The N = 1 and N = 2 superconformal algebras are discussed in the pertinent cases.

Bethe ansatz solutions for Temperley-Lieb quantum spin chains

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups U-q(X-n) for X-n = A(1), B-n, C-n and D-n. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, bleak quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

ANOMALIES IN CURVED SPACETIME AT FINITE TEMPERATURE

We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting lambdaphi4 and chiral Schwinger models in curved backgrounds at finite temperature.

Virial coefficients from (2+1)-dimensional QED effective actions at finite temperature and density

From spinor and scalar (2 + 1)-dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These coefficients depend on a parameter theta related to the time-component of the gauge field, which plays an essential role for large gauge invariance. The variation of the parameter theta might lead to an interpolation between fermionic and bosonic virial coefficients, although these coefficients are singular for theta = pi/2.

Symplectic actions on coadjoint orbits

We present a compact expression for the field theoretical actions based on the symplectic analysis of coadjoint orbits of Lie groups. The final formula for the action density α c becomes a bilinear form 〈(S, 1/λ), (y, m y)〉, where S is a 1-cocycle of the Lie group (a schwarzian type of derivative in conformai case), λ is a coefficient of the central element of the algebra and script Y sign ≡ (y, m y) is the generalized Maurer-Cartan form. In this way the action is fully determined in terms of the basic group theoretical objects. This result is illustrated on a number of examples, including the superconformal model with N = 2. In this case the method is applied to derive the N = 2 superspace generalization of the D=2 Polyakov (super-) gravity action in a manifest (2, 0) supersymmetric form. As a byproduct we also find a natural (2, 0) superspace generalization of the Beltrami equations for the (2, 0) supersymmetric world-sheet metric describing the transition from the conformal to the chiral gauge.

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Gauge-independent analysis of 2D-gravity

In this note we show that the induced 2D-gravity SL(2, ℝ) currents can be defined in a gauge-independent way although they manifest themselves as generators of residual symmetries only in some special gauges. In the Coulomb gas representation we investigate two approaches, namely one resembling string field theory and another that emphasizes the SL(2, ℝ) structure in the phase space. In the conformal gauge we propose a solution of the Liouville theory in terms of the SL(2, ℝ) currents.

New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

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.

Affine Toda systems coupled to matter fields

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to -l (l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a hamiltonian reduction procedure from the so-called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to nonzero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories possess a U(1 ) Noether current, which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one-dimensional bag model for QCD. These models are also relevant to the study of electron self-localization in (quasi-)one-dimensional electron-phonon systems.

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.