Quasi-local Update Algorithms for Numerical Simulations of d=3 SU(2) LGT in the Dual Formulation

In the dual formulation of d=3 SU(2) LGT, the link variables are group representations and valid configurations are those satisfying a number of triangle inequalities. In \cite{lat99} algorithms for local updates that automatically respect these constraints were described. It was also pointed out there that these local updates were not ergodic. In this presentation, we describe two different quasi-local updating algorithms which, in conjunction with the local updates, appear to be ergodic.Comment: LATTICE2000(Topics in Gauge Theories),5 pages,5 figures,LaTe

Reformulating Yang-Mills theory in terms of local gauge invariant variables

An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of metrics on 3 manifolds.Comment: Lattice 2000 (Gravity and Matrix Models) 3 pages, espcrc2.st

Quark Propagator and Chiral Symmetry with String Tension

General properties of the light and heavy quark propagators have been investigated in the context of string tension interaction. Confinement, chiral symmetry breaking, spectral properties of the propagator are analytically studied and numerically validated. We show that the propagator is analytic in the infrared region even for massless quarks with a non zero radius of convergence. Emergence of more than one mass scale is exemplified. Massless limit of the quark propagator does exhibit critical behaviour.Comment: 15 pages, 6 eps figures, LaTe

Mesons: Relativistic Bound States with String Tension

A systematic method of analysing Bethe-Salpeter equation using spectral representation for the relativistic bound state wave function is given. This has been explicitly applied in the context of perturbative QCD with string tension in the $1 \over N$ expansion. We show that there are only a few stable bound state mesons due to the small "threshold mass"(constituent mass) of quarks. The asymptotic properties of the bound states are analytically analysed. The spectrum is derived analytically and compared phenomenologically. Chiral symmetry breaking and PCAC results are demonstrated. We make a simple minded observation to determine the size of the bound states as a function of the energy of the boundstate.Comment: 14 pages, 2 eps figures, LaTe

Current Status of the Numerical Simulations of d=3 SU(2) Lattice Gauge Theory in the Dual Formulation

We have continued our systematic investigations of the numerical simulations of lattice gauge theories in the dual formulation. These include: i) a more practical implementation of the quasi-local updating technique, ii) a thorough investigation of the sign problem, iii) issues related to the ergodicity of the various update algorithms, iv) a novel way of measuring conventional observables like plaquette in the dual formalism and v) investigations of thermalisation. While the dual formulation holds out a lot of promises in principle, there are still some ways to go before it can be made into an attractive alternative lattice formulation.Comment: LATTICE2000(Topics in Gauge Theories),5 pages,3 figures,LaTex(espcrc2.sty