The depletion potential in one, two and three dimensions

We study the behavior of the depletion potential in binary mixtures of hard particles in one, two, and three dimensions within the framework of a general theory for depletion potential using density functional theory. By doing so we extend earlier studies of the depletion potential in three dimensions to the cases ofd = 1 and 2 about which little is known, despite their importance for experiments. We also verify scaling relations between depletion potentials in sphere-sphere and wall-sphere geometries ind = 3 and in disk-disk and wall-disk geometries ind = 2, which originate from geometrical considerations.     

From geometric quantization to conformal field theory

Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant)r-matrices and this geometrical approach.     

The electrical conductivity of binary disordered systems,percolation clusters,fractals and related models

We review theoretical and experimental studies of the AC dielectric response of inhomogeneous materials, modelled as bond percolation networks, with a binary (conductor-dielectric) distribution of bond conductances. We first summarize the key results of percolation theory, concerning mostly geometrical and static (DC) transport properties, with emphasis on the scaling properties of the critical region around the percolation threshold. The frequency-dependent (AC) response of a general binary model is then studied by means of various approaches, including the effective-medium approximation, a scaling theory of the critical region, numerical computations using the transfer-matrix algorithm, and several exactly solvable deterministic fractal models. Transient regimes, related to singularities in the complex-frequency plane, are also investigated. Theoretical predictions are made more explicit in two specific cases, namely R-C and RL-C networks, and compared with a broad variety of experimental results, concerning, for example, granular composites, thin films, powders, microemulsions, cermets, porous ceramics and the viscoelastic properties of gels.     

Hydrodynamics in theO 4 gravity

We develop hydrodynamics in a new geometrical gravitational theory, calledO ₄ gravity, which we recently proposed. According to this formulation, matter is not necessarily conserved. The nonconservation of matter might have been considerable in an early era of cosmological evolution.     

Variational principle for theP(4) affine theory of gravitation and electromagnetism

We propose a Lagrangian for theP(4) theory of gravitation and electromagnetism which is a straightforward generalization of the Einstein Lagrangian. A constrained Palatini variation of this Lagrangian yields the geometrical Einstein-Maxwell affine field equations. We show that these results can be extended easily to include both electric and magnetic charges. Finally, we consider conservation laws arising from the invariance properties of the Lagrangian.     

Cartan's geometrical structure of supergravity

We emphasise the geometrical partnership of the vierbein and the spin3/2 field in the structure of the supergrvity Lagrangian. Both fields are introduced as components of the same matrix differential form. The only local symmetry of the theory is SL(2,C).To be submitted for publication.     

Krichever Maps,Faà di Bruno Polynomials,and Cohomology in KP Theory

We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.     

Biframe bundle geometry: An extension of Rainich-Misner-Wheeler theory to include sources

Recently the original theory of Rainich, Misner, and Wheeler (RMW) has been shown to have a natural reformulation in terms of a new principal fiber bundle, namely the bundle of biframesL ² M over spacetime. We extend this new formalism further and show that the original RMW program can be generalized to include Einstein-Maxwell spacetimes with geometrical sources. The assumptions of a Riemannian connection one-form on the linear frame bundleLM and a general connection one-form onL ² M necessarily imply the existence of a difference formK. A generalization of the standard RMW theorem is developed which provides the necessary and sufficient conditions on an arbitrary triple (M, g, K) in order for this triple to be an Einstein-Maxwell spacetime with geometrical sources. All sources for the field equations associated with such spacetimes are geometrical, as they are constructible from the metricg, the difference formK, and their derivatives. The extension of the RMW program presented here introduces a second complexion vector, in addition to the standard RMW complexion vector, and the formalism reduces, in the special case of no sources, to the standard RMW program.     

A generalization of the non-linear λ-model to four dimensions

The two-dimensional O(3)-nonlinear σ-model is generalized to four dimensions. The generalization, which includes three related models of the types O(5), CP² and HP¹, preserves conformal invariance and many of the geometrical properties of the non-linear σ-model. We examine the topological and geometrical properties of the O(5)-model in detail and, in particular, investigate its close connection with the Yang-Mills theory. The instantons of the model are examined and shown to correspond to conformal mappings from R⁴ into S⁴.     

The electronic and magnetic properties of （Mn,C）-codoped ZnO diluted magnetic semiconductor

The electronic and magnetic properties of (Mn,C)-codoped ZnO are studied in the Perdew-Burke-Ernzerhof form of generalized gradient approximation of the density functional theory. By investigating five geometrical configurations, we find that Mn doped ZnO exhibits anti-ferromagnetic or spin-glass behaviour, and there are no carriers to mediate the long range ferromagnetic (FM) interaction without acceptor co-doping. We observe that the FM interaction for (Mn,C)-codoped ZnO is due to the hybridization between C 2p and Mn 3d states, which is strong enough to lead to hole-mediated ferromagnetism at room temperature. Meanwhile, we demonstrate that ZnO co-doped with Mn and C has a stable FM ground state and show that the (Mn,C)-codoped ZnO is FM semiconductor with super-high Curie temperature (T C = 5475 K). These results are conducive to the design of dilute magnetic semiconductors with codopants for spintronics applications.     

Reconsiderations on the formulation of general relativity based on Riemannian structures

We prove that some basic aspects of gravity commonly attributed to the modern connection-based approaches, can be reached naturally within the usual Riemannian geometry-based approach, by assuming the independence between the metric and the connection of the background manifold. These aspects are: 1) the BF-like field theory structure of the Einstein–Hilbert action, of the cosmological term, and of the corresponding equations of motion; 2) the formulation of Maxwellian field theories using only the Riemannian connection and its corresponding curvature tensor, and the subsequent unification of gravity and gauge interactions in a four dimensional field theory; 3) the construction of four and three dimensional geometrical invariants in terms of the Riemann tensor and its traces, particularly the formulation of an anomalous Chern–Simons topological model where the action of diffeomorphisms is identified with the action of a gauge symmetry, close to Witten’s formulation of three-dimensional gravity as a Chern–Simon gauge theory. 4) Tordions as propagating and non-propagating fields are also formulated in this approach. This new formulation collapses to the usual one when the metric connection is invoked, and certain geometrical structures very known in the traditional literature can be identified as remanent structures in this collapse.     

Large <Emphasis Type="Italic">N</Emphasis> Expansion of <Emphasis Type="Italic">q</Emphasis>-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.     

One-loop divergences in chiral perturbation theory and right-invariant metrics onSU(3)

In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics onSU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic fild is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at orderO(p ⁴) allows to derive some relations between thefinite parts of the coupling constants. These relations do not depend on the scale used to renormalize.     

Tetrad fields and metric tensor in the gauge theory of gravitation

The most relevant geometrical aspects of the gauge theory of gravitation are considered. A global definition of the tetrad fields is given and emphasis is placed on their role in defining an isomorphism between the tangent bundle of space-time and an appropriate vector bundle B associated to the gauge bundle. It is finally shown how to construct the fundamental geometrical objects on space-time, starting from B.     

Lagrangian formulation of a geometrical scalar-tensor theory of gravitation

The author's geometrical theory of the scalar-tensor gravitational field is extended by formulating it in terms of a Lagrangian. An exact solution of the coupled nonlinear field equations for a static point mass is also presented. This theory which is conformally equivalent to the empty spaceEinstein equations predicts the same results for experiments as the usual theory of Brans and Dicke which has a non-zero energy momentum tensor.     

Geometrization in the Yang-Mills extended supergravity and Klein-Kaluza versions

We relate personal encounters of three kinds with geometrical approaches, in the development of a relativistic quantum field theory of the fundamental interactions—including interactions with Nathan Rosen. We characterize the geometrical structures involved and discuss the more recent attempts to develop a unified theory based on a Klein-Kaluza contraction of the eightfold extended supergravity.Invited paper, dedicated to Nathan Rosen on the occasion of his seventy-fifth birthday.On leave from Tel Aviv University, Israel, and the University of Texas at Austin, Texas.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.