相关论文: Preparation for Gauge Theory

Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.

There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…

We present a mathematical framework of gauge theories that is based upon a skew-adjoint Lie algebra and a generalized Dirac operator, both acting on a Hilbert space.

The classical theory of Riemann ellipsoids is formulated naturally as a gauge theory based on a principal G-bundle ${\cal P}$. The structure group G=SO(3) is the vorticity group, and the bundle ${\cal P}=GL_+(3, R})$ is the connected…

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…

The main purpose of these lecture notes is to provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming mostly at advanced undergraduate and graduate students. In addition, the connection between…

We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…

Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…

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…

The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…

Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings) using 2-connections on 2-bundles. A 2-bundle…

We formulate the most general gravitational models with constant negative curvature ("hyperbolic gravity") on an arbitrary orientable two-dimensional surface of genus $g$ with $b$ circle boundaries in terms of a $\text{PSL}(2,\mathbb…

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…

This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent…

We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…

In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…

This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…

This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…

This paper is a mixture of expository material and current research material. Among new results are examples of generalised harmonic spinors and their gauged version, the generalised Seiberg-Witten equations.