Exactly soluble peierls models

Exactly soluble models for electrons on a deformable discrete chain are found. They include typical continuous Peierls models as special limits. The chain structure, electronic spectrum and thermodynamic functions in the ground state are found. The region of a nearly half filled band corresponding to the polyacetylene model is described in detail.     

Exactly soluble anharmonic potential models

The construction and exact quantum mechanical solution of anharmonic potential models is discussed. For low energy eigenvalues the proposed models simulate the usual quadratic-quartic potentials, but for high eigenvalues their properties are essentially those of the harmonic oscillator.     

Connecting T-duality invariant theories

We show that the vanishing of the one-loop beta-functional of the doubled formalism (which describes string theory on a torus fibration in which the fibres are doubled) is the same as the equation of motion of the recently proposed generalised metric formulation of double field theory restricted to this background: both are the vanishing of a generalised Ricci tensor. That this tensor arises in both backgrounds indicates the importance of a new doubled differential geometry for understanding both constructions.     

Exactly soluble models for distortive structural phase transitions

We examine three exactly soluble models for systems undergoing a structural phase transition. Two models are described by a lattice-dynamic hamiltonian, the phase transition being driven by a spherical constraint in one case and by a long-range anharmonic interaction in the other. Finally, we treat a continuous model based on an effective free energy for the long-wavelength fluctuations of the order-parameter field, which may be obtained by eliminating the other non-critical degrees of freedom. The static critical exponents are those of the spherical Kac model in all three cases, whereas the dynamic critical behaviour strongly depends on the time reversal properties of the underlying equation of motion.     

Exactly soluble multidimensional Fokker-Planck equations with nonlinear drift

The time-dependent analytic solutions of three classes of multidimensional Fokker-Planck equations with nonlinear drift are presented together with eigenvalues which are complex and depend essentially on the correlation functions of the fluctuations.     

Exactly soluble planar Ising models on compressible lattices

Two planar Ising models on compressible lattices are considered. The elastic forces act in the horizontal direction only and between nearest-neighbors, but are otherwise arbitrary. The nearest-neighbor exchange interaction is taken as constant for two spins with the same column index and depending on separation for spins on the same row. In the first model (A) the transition remains continuous, and Fisher's theory of renormalized exponents applies; in the second model (B) the additional constraint that spins on a column move as a unit changes the transition to first order.     

Exactly soluble multichannel scattering problems with Coulomb interactions

A general separable potential approach to elastic and inelastic scattering processes is developed which takes account of Coulomb interactions in an exact way. Effective nuclear interactions are used that are separable in the channel relative motion variables and take explicit account of the coupled-channel nature of the problem. After solving the coupled-channel integral equations by means of both matrix inversion techniques and a suitable channel-decoupling procedure, we arrive at exact manageable expressions of the Coulomb-corrected nuclear transition amplitudes.     

Exactly soluble magnetoelastic lattice with a magnetic phase transition

We examine the soluble magnetoelastic Ising model developed by Baker and Essam and give a detailed discussion of its thermodynamic properties. Particular attention is devoted to the properties of the magnetic phase transition at zero field, which is found to be either first order or second order, depending on whether the experiment is performed at negative or positive pressure.Part of this work was done while L. G. was visiting Tel Aviv University. Research supported by National Science Foundation Grant No. GP. 16025 to L. G.     

Unified gauge theories and bilinear invariant forms

Gauge theories based on a simple Lie algebra orU(1) have only one coupling constant. It is shown that there are no other Lie algebras with this property.     

Two-dimensional conformal invariant theories on a torus

The study of unitary conformal invariant theories on a torus reveals two important properties: the partition function and correlation functions may be expressed in terms of free (gaussian) field modes, and the modular invariance dictates the operator content of the theory: for a generic value of the central charge c = 1−/m(m + 1), there exist at least two distinct models depending whether m = 0,3 mod or m = 1,2 mod 4. The case of non-unitary c < 1 theories is also briefly discussed.     

Canonical dimensions in asymptotically conformal invariant theories

It is shown that canonical dimensions in the product of currents near the light-cone imply a free field structure for the Wightman functions of currents in the underlying skeleton theory.     

Dynamical mass generation in BRS invariant theories

The problem of the origin of the gauge particle's mass is considered in the framework of the BRS symmetry. A new approach is suggested where the global gauge group symmetry of the quantum theory is hidden by the condensation of bound states of the ghost fields in the perturbative vacuum. Dynamical mass generation for the gauge fields follows the Schwinger mechanism.     

Conformal field theories and modular invariant partition functions for parafermion field theories

Parafermion conformal field theories with D_2N discrete symmetry are examined in detail. The structure of field space of parafermion field theories is studied with the help of a projection operator G. Characters of the representations of the twist sector of parafermion algebra and projected characters are given. A new class of modular invariant partition functions, therefore conformal field theories, for parafermion theories are found. We argue that the principal theories correspond to the generic critical SOS models of Andrew, Baxter and Forrest.     

Some remarks on conformal invariant theories on four-lorentz manifolds

Contrary to the eleven-parameter group consisting of Poincaré-transformations and dilatations, the group of so-called special conformal transformations can act on the Minkowski space only as a local conformal Lie transformation group. We show that the universal covering space of the compactified Minkowski space , together with an appropriate metric \(\tilde g\) on it, form a suitable Lorentz manifold that admits universal covering group of the “conformal group” of as a transitive Lie transformation group. This group respects the causality notion on usually defined on a Lorentz manifold. However, possesses only seven isometries in contrast to the well-known ten isometries on the Minkowski space , which correspond to conservation of energy-momentum and angular-momentum.     

Symmetries of SU(2) invariant Yang-Mills theories

It is shown that both the field equations and the self-duality equations of SU(2) invariant Yang-Mills theories do not allow any other Lie symmetries than those they have by construction, i.e., the 15 generators of the conformal group and the 3 generators of the gauge group. This is true in Euclidean as well in Minkowskian space-time.