arXiv subjects

Luiz Henrique P. Pêgas

Publications and source records attributed to Luiz Henrique P. Pêgas.

4 recordsLinked to original sources

arXiv2018

Lie Groupoids in Classical Field Theory I: Noether's Theorem

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.

math-ph↗

arXiv2018

Lie Groupoids in Classical Field Theory II: Gauge Theories, Minimal Coupling and Utiyama's Theorem

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. In this second part, we shall adapt the formalism developed in the first paper to the context of gauge theories and deal with minimal coupling and Utiyama's theorem.

math-ph↗

arXiv2013

Groupoids and cogroupoids: an one object approach

The aim of this paper is to provide a definition of groupoid and cogroupoid internal to a category which makes use of only one object and morphisms, in contrast with the two object approach commonly found in the literature. We will give some examples and we will establish a relation with group objects (and Hopf algebras). The definitions presented here were designed to simplify some constructions related to internalizations, Lie groupoids and Hopf algebroids.

math.CT↗

arXiv2011

About the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds

In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations on an algebra are given, allowing to work on these concepts, when the algebra is an algebra of functions on a differentiable manifold, in a coordinate free description. Also, it will be constructed a cup product on polyderivations which corresponds on (Hochschild) cohomology to wedge product on multivector fields. At the end, a proof of the above mentioned theorem will be given.

math.RA↗