Related papers: Preparation for Gauge Theory
In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splited to exact gauge invariant subsets. Arguments and examples given in the review…
The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…
An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and…
After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple…
We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan)…
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport)…
A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies,…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…
We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with $A_{N-1}$ gauge algebra and different…
An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric…
In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to…