the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

1. Introduction. John von Neumann's brilliant mind blazed over lattice theory like a meteor, during a brief period centering around 1935-1937. With the aim of interesting him in lattices, I had called his attention, in 1933-1934, to the fact that the sublattice generated by three subspaces of Hubert space (or any other vector space) contained 28 subspaces in general, to the analogy between dime...

These are the proceedings of the workshop on “Lattice QCD, Chiral Perturbation Theory and Hadron Phenomenology” held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas from October 2 to 6, 2006. The workshop concentrated on bringing together researchers working in lattice QCD and chiral perturbation theory with the aim of improving our understanding how hadron p...

One approach to field theory, in particular to aspects that are not well treated in perturbation theory, is to approximate the field defined on a spacetime continuum with a lattice field theory, defined on a lattice of space-time points. There has been a great deal of cross-fertilization from considering renormalization from the continuum high-energy physics point of view and from the condensed...

We show how the abstract theory of (complete, boolean) lattices can be for-malised as a theory in the HOL theorem prover. The abstract lattice theory can be instantiated for concrete cases, providing immediate instantiations of many useful results. In particular, we treat the abstract theory of function lattices as an instantiation of the abstract lattice theory.

Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distr...

We study the one–loop renormalization of noncommutative U (N) gauge theories without matter. We find that for N > 1 the renormalization of the four-point function requires a counterterm which is not present in ordinary gauge theories and breaks the noncommutative gauge invariance. This counterterm is reminiscent of a nonplanar contribution in string theory.

In this tutorial, I will discuss the concepts behind generalizing ordering to measuring and apply these ideas to the derivation of probability theory. The fundamental concept is that anything that can be ordered can be measured. Since we are in the business of making statements about the world around us, we focus on ordering logical statements according to implication. This results in a Boolean...