A note on noncommutative Chern–Simons model on manifolds with boundary

We study field theories defined in regions of the spatial noncommutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half-plane. We find that classical consistency and gauge invariance lead necessary to the introduct...

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Detalles Bibliográficos
Autor principal: Lugo, Adrián René
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2002
Materias:
Física
Ciencias Exactas
Chern-simons theories
Non-commutative theories
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/104700
http://hdl.handle.net/11336/99141
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-104700
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Ciencias Exactas
Chern-simons theories
Non-commutative theories
spellingShingle Física
Ciencias Exactas
Chern-simons theories
Non-commutative theories
Lugo, Adrián René
A note on noncommutative Chern–Simons model on manifolds with boundary
topic_facet Física
Ciencias Exactas
Chern-simons theories
Non-commutative theories
description We study field theories defined in regions of the spatial noncommutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half-plane. We find that classical consistency and gauge invariance lead necessary to the introduction of K0-space of square integrable functions null together with all their derivatives at the origin. Furthermore the requirement of closure of K<sub>0</sub> under the *-product leads to the introduction of a novel notion of the *-product itself in regions where a boundary is present, that in turn yields the complexification of the gauge group and to consider chiral waves in one sense or other. The canonical quantization of the theory is sketched identifying the physical states and the physical operators. These last ones include ordinary NC Wilson lines starting and ending on the boundary that yield correlation functions depending on points on the one-dimensional boundary. We finally extend the definition of the *-product to a strip and comment on possible relevance of these results to finite quantum Hall systems.
format Articulo
Preprint
author Lugo, Adrián René
author_facet Lugo, Adrián René
author_sort Lugo, Adrián René
title A note on noncommutative Chern–Simons model on manifolds with boundary
title_short A note on noncommutative Chern–Simons model on manifolds with boundary
title_full A note on noncommutative Chern–Simons model on manifolds with boundary
title_fullStr A note on noncommutative Chern–Simons model on manifolds with boundary
title_full_unstemmed A note on noncommutative Chern–Simons model on manifolds with boundary
title_sort note on noncommutative chern–simons model on manifolds with boundary
publishDate 2002
url http://sedici.unlp.edu.ar/handle/10915/104700
http://hdl.handle.net/11336/99141
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