Related papers: Field Theory for Multiple Integrals

In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville…

A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the…

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…

Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…

We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…

These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of…

This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

The field theory Galilean symmetry, which was introduced in the context of modified gravity, gives a neat way to construct Lorentz-covariant theories of a scalar field, such that the equations of motion contain at most second-order…

The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…

We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in an infinite-dimensional group, which…

We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…

Following the formuation of Borcherds, we develop the theory of (quantum) vertex algebras, including several concrete examples. We also investigate the relationship between the vertex algebra and the chiral algebra due to Beilinson and…

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the…

A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…

We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,....…

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…