Critical exponents and elementary particles

Particles are shown to exist for a.e. value of the mass in single phase ⁴ lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequalitydm ²/dZ, where =m ₀ ² is a bare mass² andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.Supported in part by the National Science Foundation under grant PHY 76-17191Supported in part by the National Science Foundation under grant MPS 75-21212     

Bounds on eigenvalues of the product and the Jordan product of two positive definite operators on a finite-dimensional Hilbert space

We show that R ²ⁿ with its standard symplectic structure is universal in that, subject to a mild topological restriction, essentially all symplectic manifolds can be obtained from it by reduction.Ford Foundation Fellow. Partially supported by NSF grant # DMS-8805699.Supported by the Netherlands Organization for Scientific Research (NWO).     

Sewing Polyakov amplitudes I: Sewing at a fixed conformal structure

We consider the problem of reconstructing the correlation functions of a conformal field theory on a surface from the correlation functions on a surface obtained from by cutting along a closed curve. We show that under quite general conditions, the correlation functions on the cut surface can be sewn by integrating over appropriate boundary valuess of the field.Supported in part by DOE grant DE-AC02-76ERO2220Supported in part by DOE grant DE-AS06-88ER40423     

Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds

The purpose of this paper is to construct non-perturbative deformation quantizations of the algebras of smooth functions on Poisson supermanifolds. For the examplesU ^1¦1 andC ^m¦n , algebras of super Toeplitz operators are defined with respect to certain Hilbert spaces of superholomorphic functions. Generators and relations for these algebras are given. The algebras can be thought of as algebras of quantized functions, and deformation conditions are proven which demonstrate the recovery of the super Poisson structures in a semi-classical limit.Supported in part by the Department of Energy under grant DE-FG02-88ER25065Supported in part by the Italian National Institute for Nuclear Physics (INFN)     

A spin-statistics theorem for composites containing both electric and magnetic charges

The present paper states and proves an asymptotic spin-statistics theorem for composites consisting of electrically and magnetically charged particles. We work in the framework of a nonrelativistic theory, taking as the classical configuration space aU(1) bundle over the space of physical configurations, and as the quantum hilbert space the homogeneous square integrable functions on that bundle. The theorems are proved using a formalism we develop here for treating gauge spaces —U(1) bundles with connections; in particular, two products related to tensor products of vector bundles prove to be extremely useful in displaying the structure of the gauge spaces that naturally arise in this theory.Supported in part by the National Science Foundation under grant number PHY 77-07111Supported in part by the National Science Foundation under grant number PHY 78-24275     

High order corrections to the time-dependent Born-Oppenheimer approximation. II: Coulomb systems

We study the dynamics of molecular systems with Coulomb forces. We prove that if the nuclear masses are proportional to ^–4, then certain solutions to the time dependent Schrödinger equation have asymptotic expansions to arbitrarily high order in powers of , as 0.Supported in part by the National Science Foundation under grant number DMS-8601536     

Quasifinite highest weight modules over the Lie algebra of differential operators on the circle

We classify positive energy representations with finite degeneracies of the Lie algebraW ₁₊ and construct them in terms of representation theory of the Lie algebra of infinites matrices with finite number of non-zero diagonals over the algebraR _m =[t]/(t ^m+1). The unitary ones are classified as well. Similar results are obtained for the sin-algebras.Supported in part by NSF grant DMS-9103792Supported in part by DOE grant DE-F602-88ER25066     

Ann-dimensional Borg-Levinson theorem

We show that the potentialq is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator –+q with Dirichlet boundary conditions on a bounded domain in ⁿ . This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.Supported by NSF grant DMS-8602033Supported by NSF grant DMS-8600797Supported by NSF grant DMS-8601118 and an Alfred P. Sloan Research Fellowship     

Quantum Riemann surfaces: II. The discrete series

We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of ^*-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional ^*-algebras.Supported by DOE under Grant DE-FG02-88ER25065.     

Strangeness production at low Q2 in deep-inelastic ep scattering at HERA

The production of neutral strange hadrons is investigated using deep-inelastic scattering events measured with the H1 detector at HERA. The measurements are made in the phase space defined by the negative four-momentum transfer squared of the photon 2<Q ²<100 GeV² and the inelasticity 0.1<y<0.6. The K _s ⁰ and production cross sections and their ratios are determined. K _s ⁰ production is compared to the production of charged particles in the same region of phase space. The Λ– asymmetry is also measured and found to be consistent with zero. Predictions of leading order Monte Carlo programs are compared to the data. Deceased. Supported by the Bundesministerium für Bildung und Forschung, FRG, under contract numbers 05 H1 1GUA/1, 05 H1 1PAA/1, 05 H1 1PAB/9, 05 H1 1PEA/6, 05 H1 1VHA/7 and 05 H1 1VHB/5. Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council. Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy. Partially Supported by Polish Ministry of Science and Higher Education, grant PBS/DESY/70/2006 and grant N202 2956 33. Supported by the Deutsche Forschungsgemeinschaft. Supported by VEGA SR grant no. 2/7062/27. Supported by the Swedish Natural Science Research Council. Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-1P05LA259 and MSM0021620859. Supported by the Swiss National Science Foundation. Supported by CONACYT, México, grant 48778-F. This project is co-funded by the European Social Fund (75%) National Resources (25%)—(EPEAEK II)—PYTHAGORAS II. Also at Physics Department, National Technical University, Zografou Campus, 15773 Athens, Greece. Also at Rechenzentrum, Universit?t Wuppertal, Wuppertal, Germany. Also at University of P.J. Šafárik, Košice, Slovak Republic. Also at Comenius University, Bratislava, Slovak Republic. Also at CERN, Geneva, Switzerland. Also at Max-Planck-Institut für Physik, München, Germany. Also at DESY and University Hamburg, Helmholtz Humboldt Research Award. Also at Faculty of Physics, University of Bucharest, Bucharest, Romania. Supported by a scholarship of the World Laboratory Bj?rn Wiik Research Project. Also at Ulaanbaatar University, Ulaanbaatar, Mongolia.     

Decay of correlations in surface models

A convergent low-temperature expansion for a variety of models of twodimensional surfaces is presented. It yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz =e ^– In addition, the estimates give exponential decay of truncated correlations, which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue. Two particular examples included in the general framework are the solid-on-solid and discrete Gaussian models.Supported in part by the National Science Foundation under grant No. PHY 79-16812.     

The behaviour of eigenstates of arithmetic hyperbolic manifolds

In this paper we study some problems arising from the theory of Quantum Chaos, in the context of arithmetic hyperbolic manifolds. We show that there is no strong localization (scarring) onto totally geodesic submanifolds. Arithmetic examples are given, which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom.Supported by NSF grant DMS-9102082     

Bethe Algebra of Homogeneous <Emphasis Type="Italic">XXX</Emphasis> Heisenberg Model has Simple Spectrum

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional -modules. As a byproduct we show that there exist exactly two-dimensional vector subspaces with a basis such that deg f = l, deg g = n − l + 1 and f (u)g(u − 1) − f (u − 1)g(u) = (u + 1) ⁿ . Supported in part by NSF grant DMS-0601005. Supported in part by RFFI grant 08-01-00638. Supported in part by NSF grant DMS-0555327.     

New far infrared laser lines obtained by optically pumping13CD3OD

We have obtained laser action on 34 far infrared lines for the first time in fully deuterated methyl alcohol with the¹³C isotope (¹³CD₃OD), and we have measured the frequency of 13 lines. The molecule was pumped by a cw CO₂ laser. We have measured the wavelength, the relative polarization, the relative intensity of most lines, the frequency, and the CO₂ pump frequency offset of the strongest lines. The new lines are distributed in the wavelength region from 75.27 m to 464.7 m.Supported in part by a joint grant with the U.S. National Science Foundation grant # INT 80-19014 and the Brazilian Conselho Nacional de Pesquisas (CNPq).     

The bicovariant differential calculus on the κ-Poincaré group and on the κ-Minkowski space

The bicovariant differential calculus on the four-dimensional-Poincaré group and the corresponding Lie-algebra like structure are described. The differential calculus on then-dimensional-Minkowski space covariant under the action of the-Poincaré group is constructed.Presented at the 4^th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2 P 302 217 06 p 02Supported by KBN grant 2 P 302 867 06     

Wedges I

The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results—hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a -sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function.Supported in part by NSF grant PHY84-04931.Supported in part by SERC grant GR/D 15911.Supported in part by a NSERC (Canada) Fellowship.Supported in part by SERC grant B/83301669.     

The classification of monopoles for the classical groups

By studying a construction of Nahm, we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forSU(N),SO(N) andSp(N); these are found to be equivalent to spaces of holomorphic maps from ₁ into flag manifolds.Research supported in part by NSERC grant A8361 and FCAR grant EQ3518     

Quantum Riemann surfaces I. The unit disc

We construct a non-commutative ^*-algebra which is a quantum deformation of the algebra of continuous functions on the closed unit disc . is generated by the Toeplitz operators on a suitable Hilbert space of holomorphic functions onU.Supported in part by the National Science Foundation under grant DMS/PHY 88-16214     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383