Related papers: Geometrical formalism in gauge theories
Gauge symmetric methods for data representation and analysis utilize tools from the differential geometry of vector bundles in order to achieve consistent data processing architectures with respect to local symmetry and equivariance. In…
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…
A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
We make a systematic development of the non-Abelian formulation of two-form gauge fields with topological coupling with the Yang-Mills one-form connection. An analysis of the gauge structure, reducibility conditions and physical degrees of…
This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain…
We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
Supersymmetry and Yang-Mills type gauge invariance are two of the essential properties of most, and possibly the most important models in fundamental physics. Supersymmetry is nearly trivial to prove in the (traditionally…
We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to…
Contour gauges are discussed in the framework of canonical formalism. We find flux operator algebras with the structure constants of underlying Yang-Mills theory.
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…
We undertake a detailed study of the gaugings of two-dimensional Yang-Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
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…
It is well known that BRST symmetry plays a fundamental role in constructing quantum gauge theories. Yet, at the classical level, it constitutes the modern language to study constrained systems. First, this letter reviews the Sp(2)…