Energy machineries on a manifold; application to the construction of new energy representations of gauge groups
type: Item
instance of: scholarly article
title: Energy machineries on a manifold; application to the construction of new energy representations of gauge groups
zbMATH Open document ID: 0713.53062
DOI: 10.5565/PUBLMAT_34190_01
author: D. Kharzeev
published in: Publicacions Matemàtiques
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/41110
review text: Let TX, \(T^*X\) respectively denote the tangent and cotangent bundles of a smooth n-dimensional Riemannian manifold X, and let \(D(T^*)\) denote the space of real-valued compactly supported smooth 1-forms on X endowed with the Schwartz topology of compactly supported smooth sections. The concept of an energy machinery on X is defined to be a quadruplet (Y,d\(\nu\),F,q), where Y is a connected submanifold of X endowed with a strictly positive measure \(d\nu\), and F is smooth sub-bundle of TX, while \(q=(q_ x)_{x\in Y}\) is a Euclidean structure on the restricted sub- bundle \(F^ Y\), it being assumed that, for all \(\omega\), \(\omega '\) in \(D(T^*X)\), the map \[ x\to q^*_ x(\omega^ F(x),\quad \omega^{'F}(x)),\quad x\in Y, \] is \(d\nu\)-integrable. This notion, together with that of an energy structure on X, gives rise to a systematic treatment of a large class of energy representations of gauge groups, including known cases. A sufficient condition for the irreducibility of these energy representations is obtained.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 4173851
zbMATH Keywords: energy machinery
zbMATH Keywords: energy representations
zbMATH Keywords: gauge groups
reviewed by: Hanno Rund
MaRDI profile type: Publication
OpenAlex ID: W4244396386
description: scientific article; zbMATH DE number 4173851