Related papers: On Nonlinear Gauge Theories
We investigate an interplay between some ideas in traditional gauge theory and certain concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie 2-group bundle over a Lie groupoid and studying its…
We consider two simple criteria for when a physical theory should be said to be "generally covariant", and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is…
A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…
We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general -- that is, possibly non variational nor covariant -- differential equations. In…
The Hamiltonian formulation of the theory of J-bundles is given both in the Hamilton--De Donder and in the Multimomentum Hamiltonian geometrical approaches. (3+3) Yang-Mills gauge theories are dealt with explicitly in order to restate them…
This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to…
It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge $A_{0}=0$ one should place on every link the cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
We study noncommutative principal bundles (Hopf-Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space…
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions,…
There is the notion of action Lie algebroids, containing information about Lie algebras and their actions, which is why it is natural to generalise gauge theories to a formulation using Lie algebroids; these allow structure functions in…
In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the…
We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived.…
The aim of this paper is to extend existence results for the Coulomb gauge from standard gauge theory to a non-associative setting. Non-associative gauge theory is based on smooth loops, which are the non-associative analogs of Lie groups.…
Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport,…
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional…