April 1992 arXiv papers — page 3

Taro Kashiwa, Shuji Nima, Seiji Sakoda

A method for finding Berry's phase is proposed under the Euclidean path integral formalism. It is characterized by picking up the imaginary part from the resultant exponent. Discussion is made on the generalized harmonic oscillator which is shown being so universal in a single degree case. The spin model expressed by creation and annihilation operators i

Giuseppe Bonacina, Maurizio Martellini, Mario Rasetti

We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $Σ_g\times\RrR$ with $Σ_g$ a closed and oriented Riemann surface of genus $g$, the corresponding 2+1-dimensional Euclidean quantum gravity may be related to the

Daniel Cangemi

It is shown how to couple non-relativistic matter with a Chern--Simons gauge field that belongs to a non-compact group. We treat in some details the $SL(2,{\bf R})$ and the Poincaré $ISO(2,1)$ groups. For suitable self-interactions, we are able to exhibit soliton solutions.

H. Itoyama, B. Razzaghe-Ashrafi

An ``anomalous'' supersymmetry transformation of the gaugino axial current is given in supersymmetric Yang-Mills theory. The contact term is computed to one-loop order by a gauge-invariant point-splitting procedure. We reexamine the supercurrent anomaly in this method.

Fernando Quevedo

A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauge transformations in the existence of singularities and horizons, is emphasized. A general classification of the spaces with a single time-like coordi

B. Grinstein, E. Jenkins, A. V. Manohar, M. J. Savage

The decay constants for the $D$ and $D_S$ mesons, denoted $f_D$ and $f_{D_S}$ respectively, are equal in the $SU(3)_V$ limit, as are the hadronic amplitudes for $B_S-\bar B_S$ and $B^0-\bar B^0$ mixing. The leading $SU(3)_V$ violating contribution to $\left( f_{D_S} / f_D \right)$ and to the ratio of hadronic matrix elements relevant for $B_S-\bar B_S$ and $

W. Siegel

We redo the quantization of the N=4 string, taking into account the reducibility of the constraints. The result is equivalent to the N=2 string, with critical dimension D=4 and signature (++--). The N=4 formulation has several advantages: the sigma-model field equations are implied classically, rather than by quantum/beta-function calculations; self-duality/

Stephen P. Martin

We propose a renormalizable model with no fundamental scalars which breaks itself in the manner of a "tumbling" gauge theory down to the standard model with a top-quark condensate. Because of anomaly cancellation requirements, this model contains two color sextet fermions (quixes), which are vector-like with respect to the standard model gauge group.

Daniel Z. Freedman, Gianluca Grignani, Nuria Rius, Kenneth Johnson

The conformal symmetry of the QCD Lagrangian for massless quarks is broken both by renormalization effects and the gauge fixing procedure. Renormalized primitive divergent amplitudes have the property that their form away from the overall coincident point singularity is fully determined by the bare Lagrangian, and scale dependence is restricted to $δ$-functi

Srinandan Dasmahapatra, Rinat Kedem, Barry McCoy

We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitati

T. T. Burwick, A. H. Chamseddine

The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the coupled matter system, even if the dilaton does not appear as Lagrange multiplier. Interaction terms are introduced and the s

Benjamin Grinstein, Paul F. Mende

The large mass limit of QCD uncovers symmetries that are not present in the QCD lagrangian. These symmetries have been applied to physical (finite mass) systems, such as B and D mesons. We explore the validity of this approximation in the 't Hooft model (two-dimensional QCD in the large-N approximation). We find that the large mass approximation is good,

Luis E. Ibanez, Fernando Quevedo

It has been argued that any primordial B+L asymmetry existing at very high temperatures can be subsequently erased by anomalous electroweak effects. We argue that this is not necessarily the case in the supersymmetric standard model because, apart from B and/or L, there are, above a certain temperature $T_{SS}$, two other anomalous U(1) currents. As a conseq

Marc Coppens, Takao Kato

Let $Γ$ be a plane curve of degree $d$ with $δ$ ordinary nodes and no other singularities. If $P$ is a smooth point on $Γ$ then the Weierstrass gap sequence at $P$ is considered as that at the corresponding point on the normalization of $Γ$. A smooth point $P\inΓ$ is called a total inflection point if $i(Γ,T;P)=d$ where $T$ is the tangent line to $Γ$ at $P$.

Yunping Jiang

A semigroup generated by two dimensional $C^{1+α}$ contracting maps is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives of generators and the smoothness $α$ of the generators satisfy a compatibility condition $K< 1/l^α$. We prove that the shape of the i

Wenzheng Xie

For all functions on an arbitrary open set $Ω\subset\R^3$ with zero boundary values, we prove the optimal bound \[ \sup_Ω|u| \leq (2π)^{-1/2} \left(\int_Ω|\nabla u|^2 \,dx\, \int_Ω|Δu|^2 \,dx\right)^{1/4}. \] The method of proof is elementary and admits generalizations. The inequality is applied to establish an existence theorem for the Burgers equation.

Kristian Seip

We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von Neumann lattice, and similarly, a discrete set is a set of interpolation if and onl

Subhashis Nag

In previous work it had been shown that the remarkable homogeneous space $M= \operatorname{Diff}(S^1)/\operatorname{PSL} (2,\Bbb{R})$ sits as a complex analytic and Kähler submanifold of the Universal Teichmüller Space. There is a natural immersion $Π$ of $M$ into the infinite-dimensional version (due to Segal) of the Siegel space of period matrices. That ma

Stephen C. Milne, Glenn M. Lilly

We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative ``Bailey chain&#39;&#39; concept in the setting of basic hypergeometric series very well-poised on unitary $A_{\ell}$ or symplectic $C_{\ell}$ groups. The classical case, corresponding to $A_1$ or equivalently $\roman U(2)$, contains an immense amount of the

Pierre Levy-Bruhl, Abderemane Mohamed, Jean Nourrigat

We give an estimate of the number $N(λ)$ of eigenvalues $<λ$ for the image under an irreducible representation of the ``sublaplacian&#39;&#39; on a stratified nilpotent Lie algebra. We also give an estimate for the trace of the heat-kernel associated with this operator. The estimates are formulated in term of geometrical objects related to the representation

Hendrik W. Lenstra

In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains to be done in the area. We hope to show that the study of algorithms not

Gil Kalai, Daniel J. Kleitman

The diameter of the graph of a $d$-dimensional polyhedron with $n$ facets is at most $n^{\log d+2}$

Herwig Hauser, Gerd Muller

We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the {\it tangent algebra}. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the {\it integral variety}. The paper investigates properties of this correspondence: The set of all tangent algebras is characterized in purely Lie algebra theo

Israel M. Gelfand, Robert D. MacPherson

A combinatorial formula for the Pontrjagin classes of a triangulated manifold is given. The main ingredients are oriented matroid theory and a modified formulation of Chern-Weil theory.

Eric M. Friedlander, H. Blaine Lawson

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory&#34; for complex algebraic varieties. The theory is bigraded, functorial, and admits Gysin maps. It carries a natural cup product and a pairing to $L$-homology. Chern classes of algebraic bund

Marc Burger, Jian-Shu Li, Peter Sarnak

We introduce the notion of the automorphic dual of a matrix algebraic group defined over $Q$. This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic functorial properties of this set are derived and used both to deduce arithmetic vanishing theorems of ``Ramanujan&#39;&#39; type as well as to give a new construction of automorphic

L. J. Bunce, J. D. Maitland Wright

Let $A$ be a von Neumann algebra with no direct summand of Type $\roman I_2$, and let $\scr P(A)$ be its lattice of projections. Let $X$ be a Banach space. Let $m\:\scr P(A)\to X$ be a bounded function such that $m(p+q)=m(p)+m(q)$ whenever $p$ and $q$ are orthogonal projections. The main theorem states that $m$ has a unique extension to a bounded linear oper

Ranee Brylinski, Bertram Kostant

Let $M$ be a $G$-covering of a nilpotent orbit in $\g$ where $G$ is a complex semisimple Lie group and $\g=\text{Lie}(G)$. We prove that under Poisson bracket the space $R[2]$ of homogeneous functions on $M$ of degree 2 is the unique maximal semisimple Lie subalgebra of $R=R(M)$ containing $\g$. The action of $\g&#39;\simeq R[2]$ exponentiates to an action o

Charles P. Boyer, Jacques Hurtubise, Benjamin M. Mann, R. James Milgram

The purpose of this note is to announce our proof of the Atiyah-Jones conjecture concerning the topology of the moduli spaces of based SU(2)-instantons over S^4. Full details and proofs appear in our paper [BHMM1].

Donu Arapura

Let $X$ be a compact Kähler manifold. The set $\cha(X)$ of one-dimensional complex valued characters of the fundamental group of $X$ forms an algebraic group. Consider the subset of $\cha(X)$ consisting of those characters for which the corresponding local system has nontrivial cohomology in a given degree $d$. This set is shown to be a union of finitely man

Sergio Albeverio, Zhi-Ming Ma

The theory of Dirichlet forms as originated by Beurling-Deny and developed particularly by Fukushima and Silverstein, is a natural functional analytic extension of classical (and axiomatic) potential theory. Although some parts of it have abstract measure theoretic versions, the basic general construction of a Hunt process properly associated with the form,

Olga Gil-Medrano, Peter W. Michor

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

Peter W. Michor

This is a review of [Michor, Peter W.: The moment mapping for a unitary representation, Ann. Global Anal. Geometry, 8, No 3(1990), 299--313] including a careful description of calculus in infinite dimensions. For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the d

Markus Mauhart, Peter W. Michor

The well known formula $[X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0 (\Fl^Y_{-t}ø\Fl^X_{-t}ø\Fl^Y_tø\Fl^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.

Peter W. Michor

If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a &#34;double sided semidirect product&#34;. It is called the {\it knit product} of the two subalgebras then. The integrated version of this is called a {\it knit product} of groups --- it coincides with the {\it Zappa-Szép product}. The

J. Brian Conrey, Amit Ghosh

In the study of Dirichlet series with arithmetic significance there has appeared (through the study of known examples) certain expectations, namely (i) if a functional equation and Euler product exists, then it is likely that a type of Riemann hypothesis will hold, (ii) that if in addition the function has a simple pole at the point s=1, then it must be a pr

Jari Taskinen

We show that a continuous bilinear mapping P: C(I) \times C(I) \to C(I) can be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear operators on C(I) and multiplication is defined pointwise, if and only if for all t in I the bilinear form (f,g) -> P(f,g)(t) is integral on C(I) times C(I) and depends in a sense continuously on t. To th

A. Aurilia, E. Spallucci

A metal ring removed from a soap-water solution encloses a film of soap which can be mathematically described as a minimal surface having the ring as its only boundary. This is known to everybody. In this letter we suggest a relativistic extension of the above fluidodynamic system where the soap film is replaced by a Kalb-Ramond gauge potential $\b(x)$ and t

U. Baur, M. A. Doncheski

We study the prospects of testing the $WWγ$ vertex in $e^- p\toνγX$ and $e^+ p\toνγX$ at HERA and LEP/LHC. Destructive interference effects between the Standard Model and the anomalous contributions to the amplitude severely limit the sensitivity of both processes to non-standard $WWγ$ couplings. Sensitivity limits for the anomalous $WWγ$ couplings $κ$ and $

V. Barger, Kingman Cheung, B. A. Kniehl, R. J. N. Phillips

We explore the potential of a future e^+ e^- collider in the 0.5 TeV center-of-mass energy range to detect intermediate or heavy Higgs bosons in the Standard Model. We first briefly assess the production cross sections and update the decay branching fractions for a Higgs boson of intermediate mass, with M_Z < m_H < 2M_W. We then study in detail the possibili

L. E. Ibanez, G. G. Ross

We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking