Remarks on conformal invariance

The existence of unitary representations for the special Conformal Group, is investigated for free fields in any dimension, and the connection between the correct transformation properties of the fields and weak conformal invariance pointed out.Partially supported by the Brazilian National Research Council, and K.F.A. Jülich, Germany.On leave of absence from University of Bielefeld, Bielefeld (Germany).     

Finite total cross-sections in nonrelativistic quantum mechanics

We present a simple geometric method for estimating total cross-sections in two-body and more generally two cluster scattering. We discuss a variety of aspects of total cross-sections including large coupling constant behavior.On leave from Dept. of Physics, University of Bielefeld, Federal Republic of Germany; address after April 1, 1980: Dept. of Mathematics, University of Bochum, D-4630 Bochum 1, Federal Republic of GermanyResearch partially aupported by USNSF under Grant MCS-78-01885     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Higher order perturbation theory for exponential Lagrangians: Third order

We define the vacuum expectation value of the time-ordered product of three exponentials of free massless fields as a continuous linear functional over a suitable test function space using minimal singularity as a criterion.Research sponsored by the Alfred P. Sloan Foundation.On leave from II. Institut für Theoretische Physik der Universität Hamburg, Germany.     

On the prosaic origin of the double poles in the sine-GordonS-matrix

We show that the apparently exotic double poles in the sine-GordonS-matrix are nothing but ordinary anomalous thresholds.This research was supported in part by the National Science Foundation under Grant No. PHY77-22864Max Kade Foundation Fellow. On leave of absence from the Institut für Theoretische Physik, Freie Universität Berlin, Federal Republic of Germany     

Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators

Distinguished self-adjoint extensions of Dirac operators are characterized by Nenciu and constructed by means of cut-off potentials by Wüst. In this paper it is shown that the existence and a more explicit characterization of Nenciu's self-adjoint extensions can be obtained as a consequence from results of the cut-off method, that these extensions are the same as the extensions constructed with cut-off potentials and that they are unique in some sense.On leave from Universität Zürich, Schöneberggasse 9, CH-8001 Zürich. Supported by Swiss National Science FoundationOn leave from Technische Universität Berlin, Straße des 17. Juni 135, D-1000 Berlin     

String tension and glueball mass in a lattice theory of disconnected,selfintersecting random surfaces

We exhibit the analytic structure of a model of disconnected, selfintersecting random surfaces. This model is shown to have features attractive for a Monte Carlo simulation. Previously obtained numerical data show evidence that for a 3-dim embedding space the string tension vanishes above a critical temperature and has a critical exponent between 1 and 2. The glueball mass is shown to be bounded below by the mass-gap of the 3-dim Ising model.On leave of absence from Freie Universität Berlin     

Open quantum systems with time-dependent Hamiltonians and their linear response

We give a rigorous (Hamiltonian) treatment of a quantum system weakly coupled to an infinite free reservoir and subject to an external time-dependent driving potential varying on the scale of dissipation. The linear response of the system initially in thermal equilibrium is determined and compared with the usual expressions of linear response theory.Work partly supported by NSF grant no. MPS 75-11864-A04.On leave of absence from Fachbereich Physik der Universität München. Work supported by a DFG fellowship.     

Integrability of two interactingN-dimensional rigid bodies

A new class of integrable Euler equations on the Lie algebra so(2n) describing twon-dimensional interacting rigid bodies is found. A Lax representation of equations of motion which depends on a spectral parameter is given and complete integrability is proved. The double hamiltonian structure and the Lax representation of the general flow is discussed.On leave of absence from the Institute for Theoretical Physics of Warsaw University, ul. Hoza 69, PL-00-681 Warsaw, Poland     

On the curvature of piecewise flat spaces

We consider analogs of the Lipschitz-Killing curvatures of smooth Riemannian manifolds for piecewise flat spaces. In the special case of scalar curvature, the definition is due to T. Regge; considerations in this spirit date back to J. Steiner. We show that if a piecewise flat space approximates a smooth space in a suitable sense, then the corresponding curvatures are close in the sense of measures.Supported in part by NSF MCS-810-2758-A-02Supported in part by Deutsche Forschungsgemeinschaft and NSF PHY-81-09110-A-01On leave of absence from Freie Universität Berlin     

Homogeneous Kähler manifolds: Paving the way towards new supersymmetric sigma models

Homogeneous Kähler manifolds give rise to a broad class of supersymmetric sigma models containing, as a rather special subclass, the more familiar supersymmetric sigma models based on Hermitian symmetric spaces. In this article, all homogeneous Kähler manifolds with semisimple symmetry groupG are constructed, and are classified in terms of Dynkin diagrams. Explicit expressions for the complex structure and the Kähler structure are given in terms of the Lie algebra g ofG. It is shown that for compactG, one can always find an Einstein-Kähler structure, which is unique up to a constant multiple and for which the Kähler potential takes a simple form.On leave of absence from Fakultät für Physik der Universität Freiburg, FRG     

The Jost-Schroer theorem for zero-mass fields

We extend the Jost-Schroer theorem to zero-mass fields in one time-dimension and arbitrarily many space-dimensions.On leave of absence from II. Institut für Theoretische Physik der Universität, Hamburg, Germany. Work supported by Stiftung Volkswagenwerk.     

Discretized Boltzmann equation: Lattice limit and non-Maxwellian gases

We continue the study of a discrete model of the Boltzmann equation, in which the spatial variable is replaced by a finite periodic lattice. Using a weak compactness criterion forL ₁, the existence of a lattice limit as the lattice spacing tends to zero is proved. The case of unbounded collision kernels (non-Maxwellian gases) is also treated.This work was supported in part by National Science Foundation grant no. ENG-75 15882.On leave from Mathematisches Institut der Universität München, Federal Republic of Germany     

On the spectrum of the space cut-off :P(ϕ):Hamiltonian in two space-time dimensions

We use the method of the asymptotic fields to study the spectrum of the space cut-off :P(): Hamiltonian in two space time dimensions, whereP is a semibounded polynomial.This research is partially sponsored by the Air Force Office of Scientific Research under Contract AF 49(638)1545.On leave from Matematisk Institutt, Oslo University, Norway.     

A mechanical model of Brownian motion

We consider a dynamical system consisting of one large massive particle and an infinite number of light point particles. We prove that the motion of the massive particle is, in a suitable limit, described by the Ornstein-Uhlenbeck process. This extends to three dimensions previous results by Holley in one dimension.On leave of the Institut für Theoretische Physik I der Universität Münster. Supported by a Nato fellowshipSupported by NSF Grant, No. PHY 78-03816Supported by NSF Grant, Phy 78-15920     

Exact solutions for space-times admitting non-null special conformai Killing vectors

Space-times admitting special conformai Killing vectors are studied, and some results, already existing in the literature are reviewed from a different point of view. A classification scheme for those space-times whose associated conformai factor has a non-null gradient is presented in terms of their group of isometries, giving in each case the explicit expression of their metric tensor.On leave from: Dept. de Física, Universität Illes Balears, 07071 Palma de Mallorca, Spain     

Decay and diffusion in hierarchically organized systems

The interplay of decay and diffusion in a hierarchical system is investigated studying the properties of the underlying master equation. The long time behaviour of the total number of particles in the system is analyzed and the regions in the parameter plane where the decay is diffusion-limited are determined. The influence of the decay on the diffusional spreading is also investigated.On leave from: Sektion Physik der Humboldt-Universität, Invalidenstrasse 42, DDR-1040, Berlin, German Democratic Republic     

Strict convexity of the pressure: A note on a paper of R. B. Griffiths and D. Ruelle

Strict convexity of the pressure of a quantum lattice gas is demonstrated in [1] with the help of a trace condition. An interpretation of that condition is given, and, simultaneously, an extension of the result of [1]. In particular, it is shown that the pressure is a continuous function of the lattice gas density.On leave of absence from the Institut für Theoretische Physik, Universität Göttingen, Fed. Rep. of Germany.     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

The system of six coupled, nonlinear, singular integral equations, devised by Suhl to treat the problem of a spin 1/2 magnetic impurity in a finite magnetic field is shown to be reducible to a single integral equation. Analytic properties and symmetries of the system are discussed, which may serve as a guideline for numerical studies of the final integral equation. The first few steps of an iteration in terms of the magnetic field strength are carried out analytically.On leave from the Institut für Theoretische Physik der Universität Köln.     

Asymptotic completeness for quantum mechanical potential scattering

A new (geometrical) proof is given for the asymptotic completeness of the wave operators and the absence of a singular continuous spectrum of the Hamiltonian for potentials which decrease faster than in the Coulomb case, the space dimension is arbitrary.Partially supported by a travel grant from the Deutsche ForschungsgemeinschaftOn leave from Department of Theoretical Physics, University of Bielefeld, Federal Republic of Germany