Let G be a locally compact group equipped with a left Haar measure μ, i.e. a Borel regular measure which is finite on compact, positive on open and invariant under left multiplications — by Haar’s theorem such μ exists and is unique up to normalization. The group G is called unimodular if μ is also right invariant, or equivalently if it is symmetric in the sense that μ(A) = μ(A−1) for every mea...

One of the most challenging unsolved questions that arise in the application of lattice theory to particle physics is to understand the nature of the phase structure of lattice Quantum Electrodynamics. Numerical simulations of pure gauge Lattice QED with periodic boundary conditions and using the compact gauge action S = β cos θ show the existence of a first order phase transition [1]. This avo...

This work introduces a new data structure, called Lattice-Valued Binary Decision Diagrams (or LVBDD for short), for the compact representation and manipulation of functions of the form θ : 2 7→ L, where P is a finite set of Boolean propositions and L is a finite distributive lattice. Such functions arise naturally in several verification problems. LVBDD are a natural generalisation of multi-ter...

[1] We develop a new, lattice effects-free lattice Boltzmann model for simulating crystal growth from supersaturated solution. Simulations of crystal growth from a single or multiple nuclei in a domain initially filled with supersaturated solution are presented, such as in the case of gas hydrate formation. We find that as the process changes from diffusion-controlled to surface reaction-contro...

Using the example of compact U(1) lattice gauge theory we argue that quantum link models can be used to reproduce the physics of conventional Hamiltonian lattice gauge theories. In addition to the usual gauge coupling g, these models have a new parameter j which naturally cuts-off large electric flux quanta on each link while preserving exact U(1) gauge invariance. The j → ∞ limit recovers the ...

Compact (ferroand antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions d ≥ 2. While the ferroand antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large N expansions are studied in both types of models and are argued to be asympt...

We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [1–3] can be regarded as compact formulations by using the polar decomposition of the complex link fields. In particular, the gauge part of the supersymmetric lattice action is the standard Wilson action. This formulation facilitates the construction of gauge invariant operators.