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Title: An infinite-dimensional calculus for generalized connections on hypercubic lattices

Abstract

A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior on non-generic strata is also obtained.

Authors:
 [1]
  1. IPFN - EURATOM/IST Association, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal) and CMAF, Complexo Interdisciplinar, Universidade de Lisboa, Av. Gama Pinto, 2 - 1649-003, Lisboa (Portugal)
Publication Date:
OSTI Identifier:
21501333
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 52; Journal Issue: 5; Other Information: DOI: 10.1063/1.3592919; (c) 2011 American Institute of Physics; Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FUNCTIONS; GAUGE INVARIANCE; LATTICE FIELD THEORY; MATHEMATICAL SPACE; TRIPLETS; CONSTRUCTIVE FIELD THEORY; FIELD THEORIES; INVARIANCE PRINCIPLES; MULTIPLETS; QUANTUM FIELD THEORY; SPACE

Citation Formats

Mendes, R Vilela. An infinite-dimensional calculus for generalized connections on hypercubic lattices. United States: N. p., 2011. Web. doi:10.1063/1.3592919.
Mendes, R Vilela. An infinite-dimensional calculus for generalized connections on hypercubic lattices. United States. https://doi.org/10.1063/1.3592919
Mendes, R Vilela. 2011. "An infinite-dimensional calculus for generalized connections on hypercubic lattices". United States. https://doi.org/10.1063/1.3592919.
@article{osti_21501333,
title = {An infinite-dimensional calculus for generalized connections on hypercubic lattices},
author = {Mendes, R Vilela},
abstractNote = {A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior on non-generic strata is also obtained.},
doi = {10.1063/1.3592919},
url = {https://www.osti.gov/biblio/21501333}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 5,
volume = 52,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2011},
month = {Sun May 15 00:00:00 EDT 2011}
}