By an equational theory we mean a set of equations from some fixed language which is closed with respect to logical consequences. We regard equations as universal sentences whose quantifierfree parts are equations between terms. In our notation, we suppress the universal quantifiers. Once a language has been fixed, the collection of all equational theories for that language is a lattice ordered...

Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to ribbon categories which replace the category of representations of the gauge group. This provides a framework in which the gauge group becomes a quantum group while space-time is still given by the ‘classical’ lattice. At the technical level, this construction generalizes the Spin Foam Model dual to Lattice Gauge Theor...

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...

We use perturbation theory to construct perfect lattice actions for fermions and gauge fields by blocking directly from the continuum. When one uses a renormalization group transformation that preserves chiral symmetry the resulting lattice action for massless fermions is chirally symmetric but nonlocal. When the renormalization group transformation breaks chiral symmetry the lattice action bec...

It is my privilege to introduce to this Society a vigorous and promising younger brother of group theory, by name, lattice theory. Among other things, I shall try to bring out the family resemblance. It is generally recognized that some familiarity with the notions of group, subgroup, normal subgroup, inner automorphism, commutator, and their technical properties, in a word, with group theory, ...

I review some recent theories of Physics Beyond the Standard Model whose development could benefit from lattice simulations.

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic ...

SU(2) lattice gauge theory is investigated where the traces of the Wilson lines at any lattice point and along each direction is constrained to zero. Hence, each of the lattice configurations possesses a vanishing density of heavy (anti-) quarks. The results are compared with those of pure SU(2) gauge theory which can be interpreted as the grand canonical realization of the heavy quark theory w...

We consider a (2 + 1)-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U 1 set equal to one. The term in the Hamilto-nian containing the square of the electric field in the 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this propert...

We develop quenched chiral perturbation theory for vector mesons made of light quarks, in the limit where the vector meson masses are much larger than the pion mass. We use this theory to extract the leading nonanalytic dependence of the vector meson masses on the masses of the light quarks. By comparing with analogous quantities computed in ordinary chiral perturbation theory, we estimate the ...