On the sympletic geometry of the super Teichmüller space

The geometry of the Teichmüller space of the super Riemann surfaces is examined. The Weil-Petersson Kähler form is calculated in terms of the super coordinate functions which provide local coordinates for the super Teichmüller space. It is shown that the Kähler form on the super Teichmüller space is closed.Work partially supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture No. 02302020Work partially supported by Grant-in-Aid for Scientific Research of the Ministry of Educations, Science and Culture No. 02740145     

The existence and uniqueness of solutions of Yang-Mills equations with bag boundary conditions

The Cauchy problem for the Yang-Mills equations in the Coulomb gauge is studied on a compact, connected and simply connected Riemannian manifold with boundary. An existence and uniqueness theorem for the evolution equations is proven for fields with Cauchy data in an appropriate Sobolev space. The proof is based the Hodge decomposition of the Yang-Mills fields and the theory of non-linear semigroups.Work partially supported by NSERC Research Grant A 8091Work supported by DFG Grant Schw 485/2-1     

Localization for off-diagonal disorder and for continuous Schrödinger operators

We extend the proof of localization by Delyon, Lévy, and Souillard to accommodate the Anderson model with off-diagonal disorder and the continuous Schrödinger equation with a random potential.Work supported in part by Nato under Nato Grant # 346/84Research partially supported by USNSF under grant DMS 84-16049     

A note on the power spectrum of the iterates of Feigenbaum's function

We give rigorous bounds on the scaling behaviour of the power spectrum for Feigenbaum's map.Work partially supported by the Fonds National Suisse     

Phase transitions in anisotropic lattice spin systems

A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity isnot proved, but for which the rest of the proof is valid.Work partially supported by U.S. National Science Foundation grant no. MPS 75-11864Work partially supported by U.S. National Science Foundation grant no. MCS 75-21684 A01     

A proof of part of Haldane's conjecture on spin chains

It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.Work partially supported by U.S. National Science Foundation grant PHY80-19754 and by the A.P. Sloan Foundation.Work partially supported by U.S. National Science Foundation grant PHY-85-15288.     

Yang-Mills and Dirac fields in a bag,existence and uniqueness theorems

The Cauchy problem for the Yang-Mills-Dirac system with minimal coupling is studied under the MIT quark bag boundary conditions. An existence and uniqueness theorem for the free Dirac equation is proven under that boundary condition. The existence and uniqueness of the classical time evolution of the Yang-Mills-Dirac system in a bag is shown. To ensure sufficient differentiability of the fields we need additional boundary conditions. In the proof we use the Hodge decomposition of Yang-Mills fields and the theory of non-linear semigroups.Work supported by DFG Grant Schw 485/2-1.Work partially supported by NSERC Research Grant A 8091.     

General relativity as a generalized Hamiltonian system

A rigorous setting for Dirac's generalized Hamiltonian dynamics in an infinite number of dimensions is presented. It is shown that the dynamical formulation of general relativity fits into this scheme.Work partially supported by GNFM-CNR.     

Eigentheory of the inhomogeneous Fokker-Planck equation

Ambiguities that occur in the existing eigentheory of the inhomogeneous Fokker-Planck equation are resolved. The eigenfunction expansion is shown to be identical to the known exact solution, generalizing an earlier result for the space-homogeneous case.Work partially supported by the NSF.     

Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

We construct multiparameter compact matrix pseudogroups of all types and show their representation theories are the same as their classical analogs.Work partially supported by CONICET and FAMAF (Argentina).     

How to recover causality in special relativity for tachyons

In this paper we explain why and how tachyons do not imply any causality violation within relativistic theories. Particular emphasis is given to the role of the Stückelberg-Feynman reinterpretation principle, both in ordinary physics and in tachyon physics.Work partially supported by MPI (ex-art. 286) and by CNR under contract no. 75/00442.02.     

Piezoelectric transducers as monitors for optically pumped fir lasers

The power and frequency of an optically pumped far infrared laser can be monitored by piezoelectric transducers, reliable solid state devices which detect chopped absorbed radiation by the opto-acoustic effect.Work partially supported by ONR     

The inverse problem in classical statistical mechanics

We address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system. Results are established for both the canonical and grand canonical distributions. It is shown that for essentially all systems without hard core interactions, there is a unique external potential which produces any given density. The external potential is shown to be a continuous function of the density and, in certain cases, it is shown to be differentiable. As a consequence of the differentiability of the inverse map (which is established without reference to the hard core structure in the grand canonical ensemble), we prove the existence of the Ornstein-Zernike direct correlation function. A set of necessary, but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived.Work partially supported by NSF grant PHY-8117463Work partially supported by NSF grant PHY-8116101 A01     

Mössbauer study of hydrodemetallization clay catalysts of heavy oils: Role of pyrrhotites

The evolution of iron in clay catalysts employed in hydrodemetallization (HDM) of heavy oils has been studied by the Mossbauer effect. Pyrrhotites which appear during the process, were recognized as one of the active phases in HDM.Work partially supported by CDCH (Consejo de Desarrollo Científico y Humanistico de la Universidad Central de Venezuela).     

The Thermodynamic Limit for Matter Interacting with Coulomb Forces and with the Quantized Electromagnetic Field: I. The Lower Bound

The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, was accomplished decades ago in the framework of non-relativistic quantum mechanics, . This result did not take account of interactions caused by magnetic fields, however, (the spin-spin interaction, in particular) or of the quantized nature of the electromagnetic field. Recent progress has made it possible to undertake such a proof in the context of non-relativistic QED. This paper contains one part of such a proof by giving a lower bound to the free energy that is proportional to the number of particles and which takes account of the fact that the field, unlike the particles, is never confined to a finite volume. In the earlier proof the lower bound was a ‘two line’ corollary of the ‘stability of matter’. In QED the proof is much more complicated.©2004 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.Work partially supported by U.S. National Science Foundation grant PHY 01-39984.Work partially supported by U.S. National Science Foundation grant DMS 03-00349.     

Deriving Spin of the Bosonic String1

Exploiting the strict analogy between the motion of strings and extended-like spinning particles, we propose an original kinematical formulation of the spin of bosonic strings and give, for the first time, an analytical derivation of an explicit expression of the string spin vector. ¹Work partially supported by I.N.F.N. and M. I. U. R     

Separability structures and Killing-Yano tensors in vacuum type-D space-times without acceleration

Relationships among the existence of Killing tensors, Killing-Yano tensors, and separability structures with two Killing vectors in vacuum type-D space times are investigated. It is proved that the existence of those objects is equivalent with the assumption that space-time is without acceleration.Work partially supported by GNFM of Italian National Research Council and a Polish Interdisciplinary Research Project MR-I-7.     

Stability of coulomb systems with magnetic fields

The ground state energy of an atom in the presence of an external magnetic filedB (with the electron spin-field interaction included) can be arbitrarity negative whenB is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, B ². For a hydrogenic like atom we prove that there is a critical nuclear charge,z _c , such that the atom is stable forz<z _c and unstable forz>z _c .Work partically supported by U.S. National Scinece Foundation grant DMS-8405264 during the author's stay at the Institute for Advanced Study, Princeton, NJ, USAWork partially supported by U.S. National Science Foundation grant PHY-8116101-A03Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858. Current address: Institut f. Mathematik, FU Berlin, Arnimallee 3, D-1000 Berlin 33     

Electromagnetic wave propagation in a rectangular waveguide partially loaded with magnetized planar ferrite

The propagation of electromagnetic waves in a rectangular waveguide containing a slab of transversely magnetized planar ferrite is investigated. Numerical results indicate a large differential phase shift on application of small magnetic fields when the easy plane is oriented normal to the waveguide axis. This suggests the possibility of application in ‘Remanence Operation’ at high frequencies. Work partially supported by CSIR (India).     

On the energy spectrum and parameter spaces of classicalCP n models

It is known that a large class of smooth solutions ofCP ⁿ models can be constructed starting from holomorphic maps of an algebraic curve into complex projective spaces. Here we apply results from algebraic geometry to describe the energy spectrum and the parameter spaces for such models.Work partially supported by Gruppo Nazionale di Fisica Matematica, CNR and Gruppo Nazionale per le Strutture Algebriche e Geometriche e Applicazioni, CNR