Jan Govaerts

REPRESENTATIONS OF THE ROTATION REFLECTION SYMMETRY GROUP OF THE FOUR-DIMENSIONAL CUBIC LATTICE

Abstract The structure and representations of the rotation reflection symmetry group of the four-dimensional cubic lattice are described. Their connections with the representations of the three-dimensional lattice rotation reflection group, and with the representations of the continuous O(3) and O(4) groups are given.

Superconducting properties of lead nanowires arrays

Mesoscopic superconducting lead nanowires with high aspect ratio and diameter ranging from 40 to 270 nm have been grown by electrodeposition inside nanoporous polycarbonate membranes. Nanowires with a diameter less than 50 nm were insulators due to a poor crystal structure. The others are shown to be type II superconductors because of their small electronic mean free path, instead of being type I which is usual for the bulk form of lead. An increase in the thermodynamic critical field H-c is observed and is attributed to the small transversal dimension leading to an incomplete Meissner effect. Finally, it is demonstrated that this enhancement agrees with numerical simulations based on the Ginzburg-Landau theory

Spectrum of the non-commutative spherical well

We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular, we discuss the infinite and finite non-commutative spherical wells in two dimensions. Using this, bound states and scattering can be discussed unambiguously. Here we focus on the infinite well and solution for the eigenvalues and eigenfunctions. We find that time reversal symmetry is broken by the non-commutativity. We show that in the commutative and thermodynamic limits the eigenstates and eigenfunctions of the commutative spherical well are recovered and time reversal symmetry is restored.

RADIAL EXCITATIONS AND EXOTIC MESONS VIA QCD SUM RULES

We continue our investigation of qqG states via QCD sum rules. Using previous results for the vacuum polarization functions we study both states with equal mass quarks and open flavour states for J = 0 and 1 with all possible combinations for the P and C quantum numbers, including several exotic combinations. Definite predictions are obtained in several channels. As before the resulting mass values come out high, but some of the states found can be connected to radial excitations of ordinary quarkonium states.

COVARIANT LATTICE GLUEBALL FIELDS

Abstract Fields for the creation and annihilation of gluons and glueballs, which transform irreducibly under the four-dimensional lattice rotation reflection and charge conjugation symmetry groups, are defined and discussed. The fields reduce in the zero lattice spacing limit to conventional continuum operators of definite spin, parity, and charge comjugation.

The Quantum geometer's universe: Particles, interactions and topology

With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known fundamental interactions, the physicist of the XXIst century has inherited an unfinished symphony: the unification of the quantum and the continuum. As an invitation to tomorrows quantum geometers who must design the new rulers by which to size up the Universe at those scales where the smallest meets the largest, these lectures review the basic principles of todays conceptual framework, and highlight by way of simple examples the interplay that presently exists between the quantum world of particle interactions and the classical world of geometry and topology. Comment: Lectures at the Second International Workshop on Contemporary Problems in Mathematical Physics, Cotonou, Republic of Benin, 94 pages

A MODEL FOR CHIRAL SYMMETRY BREAKING IN QCD

Abstract A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M Q , the constituent quark mass ƒ π the pion decay coupling, 〈 u u〉 , the constituent quark loop density, μ π 2 / m q , the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈 r 2 〉 π , the pion electromagnetic charge radius squared.

EXOTIC MESONS FROM QCD SUM RULES

Abstract A simple method is presented to compute the Wilson expansion coefficients for T-products in QCD with light quarks. Using this method in the framework of QCD sum rules we predict the masses of quark-antiquark-gluon states with JPC = 1−+, 0++, 1+− and 0−−.

Positron polarization in the decay of polarized N-12: a precision test of the Standard Model

The longitudinal polarization of positrons emitted along and opposite to the nuclear spin direction has been measured in the decay of polarized N-12. The results are consistent with the Standard Model prediction. In manifest left-right symmetric models this measurement provides a lower bound of 310 GeV/c(2) at 90% CL on the mass of a possible right-handed gauge boson contributing to the electroweak interaction. In generalized versions of this model our measurement provides constraints complementary to those set by high-energy experiments

Search for right-handed weak currents in the beta-asymmetry-polarization correlation from N-12 decay

Abstract The polarization of positrons emitted along and opposite to the nuclear spin direction has been measured in the decay of polarized 12 N. The results are consistent with the Standard Model prediction. In manifest left-right symmetric models this measurement provides a lower limit of 220 GeV/c 2 at 90% CL on the mass of an eventual right-handed gauge boson contributing to the electroweak interaction.