Related papers: Gauge field theories: various mathematical approac…
Yang-Mills theory is growing at the interface between high energy physics and mathematics. It is well known that Yang-Mills theory and Gauge theory in general had a profound impact on the development of modern differential and algebraic…
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant…
Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such…
We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and…
In the present article, we review the classical covariant formulation of Yang-Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We…
Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many…
In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
We revisit an old idea that gravity can be unified with Yang-Mills theory by enlarging the gauge group of gravity formulated as gauge theory. Our starting point is an action that describes a generally covariant gauge theory for a group G.…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…
In this paper, we will construct a gauge field model, in which the masses of gauge fields are non-zero and the local gauge symmetry is strictly preserved. A SU(N) gauge field model is discussed in details in this paper. In the limit $\alpha…
We propose a formulation of d-dimensional SU(N) Yang-Mills theories on a d+2-dimensional space with the extra two dimensions forming a surface with non-commutative geometry. This equivalence is valid in any finite order in the 1/N…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of…