Twisted Diff S 1-action on loop groups and representations of the virasoro algebra

A modified Hamiltonian action of Diff S ¹on the phase space LG ^C /G^C, where LG is a loop group, is defined by twisting the usual action by a left translation in LG. This twisted action is shown to be generated by a nonequivariant moment map, thereby defining a classical Poisson bracket realization of a central extension of the Lie algebra diff_C S ¹. The resulting formula expresses the Diff S ¹generators in terms of the left LG translation generators, giving a shifted modification of both the classical and quantum versions of the Sugawara formula.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the National Science Foundation.     

C*-Algebras associated with one dimensional almost periodic tilings

For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX _α with an equivalence relationR _α. OnR _α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C^*-algebra of this groupoid and show that it is the irrational rotation C^*-algebra,A _α. Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.     

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.     

The Cauchy Two-Matrix Model

We introduce a new class of two(multi)-matrix models of positive Hermitian matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann–Hilbert problems, thus paving the way to a steepest descent analysis and universality results. The interpretation of the formal expansion of the partition function in terms of multicolored ribbon-graphs is provided and a connection to the O(1) model. A steepest descent analysis of the partition function reveals that the model is related to a trigonal curve (three-sheeted covering of the plane) much in the same way as the Hermitian matrix model is related to a hyperelliptic curve. Work supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). Work supported in part by NSF Grant DMD-0400484. Work supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), Grant. No. 138591-04.     

A measurement of the τ lifetime

We have reconstructed 695 three-track τ decay vertices using a high resolution drift chamber close to the interaction point. From the distribution of decay lengths we measure the lifetime to be (3.06 ±0.20±0.14)×10⁻¹³ s. Using this result we find that the ratio of charged weak coupling constant for the τ to that of the μ,G _τ/G _μ=0.967±0.040 consistent with the concept of lepton universality. On leave from Warsaw University, Poland Now at Hasylab, DESY Supported by Bundesministerium für Forschung und Technologie Supported by UK Science and Engineering Research Council Supported by CAICYT Supported by the Minerva Gesellschaft für Forschung GmbH Supported by US Dept. of Energy, contract DE-AC02-76ER000881 and by US Nat. Sci. Foundation Grant no INT-8313994 for travel Partially supported by grant CPBP 01.06     

The short distance behavior of (φ 4)3

We consider the ₃ ⁴ quantum field theory on a torus and study the short distance behavior. We reproduce the standard result that the singularities can be removed by a simple mass renormalization. For the resulting model we give anL _p bound on the short distance regularity of the correlation functions. To obtain these results we develop a systematic treatment of the generating functional for correlations using a renormalization group method incorporating background fields.Research supported by NSF Grant DMS 9102564Research supported by NSF Grant PHY9200278.Research supported by the Natural Sciences and Engineering Research Council of Canada.     

Fusion Rules for the Vertex Operator Algebras <Emphasis Type="Italic">M</Emphasis>(1)<Superscript>+</Superscript> and <Emphasis Type="Italic">V</Emphasis><Superscript>+</Superscript><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>

The fusion rules for the vertex operator algebras M(1)⁺ (of any rank) and V⁺_L (for any positive definite even lattice L) are determined completely.Supported by JSPS Research Fellowships for Young ScientistsPartially supported by NSF grants and a research grant from the Committee on Research, UC Santa CruzPartially supported by a NSA grant and a grant from Rutgers University Research Council     

Vertex representations forN-toroidal Lie algebras and a generalization of the Virasoro algebra

Vertex representations are obtained for toroidal Lie algebras for any number of variables. These representations afford representations of certainn-variable generalizations of the Virasoro algebra that are abelian extensions of the Lie algebra of vector fields on a torus.Work supported in part by the Natural Sciences and Engineering Research Council of Canada.     

A boundary value problem for the two dimensional Broadwell model

It is shown that a certain boundary value problem for the steady two-dimensional Broadwell model on a rectangle has a solution. The boundary conditions specify the ingoing particle densities on each side of the rectangle.Research supported by the Natural Science and Engineering Research Council Canada under Grants A7847 and A8560     

A reply to arguments against a spur model for muonium formation

A clear distinction is made between the spur model for muonium formation in condensed matter and the alternative hot model. Arguments against the spur model are considered and found lacking. Some new data is presented for aqueous systems: the initial diamagnetic fraction increases with OH^– concentration, and unequivocal muonium inhibition is demonstrated for HClO₄ solutions.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

A renormalization group analysis of the Kosterlitz-Thouless phase

We consider a classical Coulomb gas with a short distance cutoff in two dimensions; equivalently a Sine-Gordon field theory. For low temperature β^-1 and low activityz the gas is in a multipole phase, the Kosterlitz-Thouless phase. For β>8π andz sufficiently small we give a complete renormalization group analysis for this phase and show that the flow of the effective measures is toward a free field (infrared asymptotic freedom). This should lead to control over the long distance behavior of the theory. Research supported by the Natural Sciences and Engineering Research Council     

On the quantization of presymplectic dynamical systems via coisotropic imbeddings

We study certain aspects of the problem of quantizing a presymplectic dynamical system. Such a system is quantized by imbedding the presymplectic manifoldM under consideration into a symplectic manifoldX and then geometrically quantizing the latter. It is known that this procedure will yield consistent results provided the imbeddingM X is coisotropic; we show that such imbeddings always exist and are locally unique. Furthermore, we investigate the extent to which the resulting quantum dynamics is independent of the choice of coisotropic imbedding; that is, we examine to what extent the presymplectic phase spaceM determines the quantum representation space and the quantization of observables. The quantization is carried out within the geometric quantization framework of Kostant and Souriau.Supported in part by the Natural Sciences and Engineering Research Council of Canada through an Operating Grant to The University of CalgarySupported in part by the Natural Sciences and Engineering Research Council of Canada through Operating Grant #A8091     

Measurement of charged current deep inelastic scattering cross sections with a longitudinally polarised electron beam at HERA

Measurements of the cross sections for charged current deep inelastic scattering in e ⁻ p collisions with longitudinally polarised electron beams are presented. The measurements are based on a data sample with an integrated luminosity of 175 pb⁻¹ collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is given for positively and negatively polarised electron beams. The differential cross-sections d σ/dQ ², d σ/dx and d σ/dy are presented for Q ²>200 GeV². The double-differential cross-section d ² σ/dxdQ ² is presented in the kinematic range 280<Q ²<30 000 GeV² and 0.015<x<0.65. The measured cross sections are compared with the predictions of the Standard Model. Deceased. Also affiliated with University College London, United Kingdom. Now at University of Liverpool, UK. On leave of absence at CERN, Geneva, Switzerland. Now at CERN, Geneva, Switzerland. Now at Bologna University, Bologna, Italy. Also at Institut of Theoretical and Experimental Physics, Moscow, Russia. Also at INP, Cracow, Poland. Also at FPACS, AGH-UST, Cracow, Poland. Partially supported by Warsaw University, Poland. Partly supported by Moscow State University, Russia. Royal Society of Edinburgh, Scottish Executive Support Research Fellow. Now at University of Salerno, Italy. Also affiliated with DESY, Germany. Also at University of Tokyo, Japan. Now at Kobe University, Japan. V. Aushev: Supported by DESY, Germany. Partly supported by Russian Foundation for Basic Research grant no. 05-02-39028-NSFC-a. STFC Advanced Fellow. Nee Korcsak-Gorzo. This material was based on work supported by the National Science Foundation, while working at the Foundation. Now at University of Kansas, Lawrence, USA. Also at Max Planck Institute, Munich, Germany, Alexander von Humboldt Research Award. Also working at Max Planck Institute, Munich, Germany. Now at KEK, Tsukuba, Japan. Now at Nagoya University, Japan. Member of Department of Radiological Science, Tokyo Metropolitan University, Japan. Now at SunMelx Co. Ltd., Tokyo, Japan. Also at Hamburg University, Inst. of Exp. Physics, Alexander von Humboldt Research Award and partially supported by DESY, Hamburg, Germany. Also at Łódź University, Poland. Member of Łódź University, Poland. Also at University of Podlasie, Siedlce, Poland. Now at Lund Universtiy, Lund, Sweden. Now at Institute of Aviation, Warsaw, Poland. Supported by the research grant no. 1 P03B 04529 (2005–2008). This work was supported in part by the Marie Curie Actions Transfer of Knowledge project COCOS (contract MTKD-CT-2004-517186). Now at University of Bonn, Germany. Now at DESY group FEB, Hamburg, Germany. Also at Moscow State University, Russia. Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).     

The Boltzmann equation: Global existence for a rare gas in an infinite vacuum

Solutions of the Boltzmann equation are proved to exist, globally in time, under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough. It is also proved, as might be expected in this case, that the density of the gas at each point in space goes to zero as time goes to infinity.Research supported by the Natural Science and Engineering Research Council Canada under Grant No. A-8560     

Theory of gauge supersymmetry in superspace

A new theory of gravity in Bose space is extended to a local gauge group of arbitrary coordinate transformations in superspace. We find that global supersymmetry can be recovered from the curved non-Riemannian superspace theory.Supported in part by the Natural Science and Engineering Research Council of Canada.     

Mössbauer measurement of the hyperfine magnetic field AT sp site in Heusler alloys Rh2 Mn Z (Z=In and Sb)

We have investigated the systematics of hyperfine magnetic field on a fixed probe at the Z-site in Heusler alloys Rh₂MnZ as the valence of Z (sp element) is varied. The hmf on¹¹⁹Sn in Rh₂MnIn_.98 ¹¹⁹Sn₀₂ has been measured at 293K and 77K. In Rh₂Mn_1.12Sb_.86 ¹¹⁹Sn_.02 the hmf on¹²¹Sb has been measured at 77 K, and on¹¹⁹Sn at 293 K and 77 K. The results are compared with the hmf on¹¹⁹Sn in Rh₂Mn Ge_.98 ¹¹⁹Sn_.02 Rh₂Mn Sn, and Rh₂Mn Pb_.98 ¹¹⁹Sn_.02.Supported by the University Research Council, University of CincinnatiSupported by the Natural Sciences and Engineering Research Council of Canada     

The Power of Quantum Systems on a Line

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses. Supported by Israel Science Foundation grant number 039-7549, Binational Science Foundation grant number 037-8404, and US Army Research Office grant number 030-7790. Supported by CIFAR, by the Government of Canada through NSERC, and by the Province of Ontario through MRI. Partially supported by NSF Grant CCR-0514082. This work was mainly done while the author was at CNRS and LRI, University of Paris-Sud, Orsay, France. Partially supported by the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST directorate as Contract Number 015848, by an ANR AlgoQP grant of the French Research Ministry, by an Alon Fellowship of the Israeli Higher Council of Academic Research, by an Individual Research grant of the ISF, and by a European Research Council (ERC) Starting Grant.     

Dual isomonodromic deformations and moment maps to loop algebras

The Hamiltonian structure of the monodromy preserving deformation equations of Jimboet al [JMMS] is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras. The nonautonomous Hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on Poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those determining the moment maps. This construction is shown to lead to dual pairs of matrix differential operators whose monodromy is preserved under the same family of deformations. As illustrative examples, involving discrete and continuous reductions, a higher rank generalization of the Hamiltonian equations governing the correlation functions for an impenetrable Bose gas is obtained, as well as dual pairs of isomonodromy representations for the equations of the Painlevé transcendentsP _V and _VI .Research supported in part by the Natural Sciences and Engineering Research Council of Canada.