An invitation to higher gauge theory

An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge ‘2-group’. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an importa...

An Invitation to String Theory

These lectures are supposed to give a point of entry into that vast web of related ideas that go under the name “string theory”. I start with a more or less qualitative introduction to gravity as a field theory and sketch how one might try to quantize it. Quantizing gravity using the usual techniques of field theory will turn out to be unsuccessful, and that will be a motivation for trying an i...

Higher Gauge Theory

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 is a categorified version of a bundle: that is, one where the fiber is not a manifold but a category with a suitable smooth structure. Where gauge theory us...

Nicolaescu An Invitation to Morse Theory – Monograph

An invitation to Quantum Game Theory

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this context, a new application of the Ising chain model is proposed.