# On the kernel of holonomy.

Publicacions Matemàtiques (1996)

- Volume: 40, Issue: 2, page 373-381
- ISSN: 0214-1493

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topCaetano, Ana Paula. "On the kernel of holonomy.." Publicacions Matemàtiques 40.2 (1996): 373-381. <http://eudml.org/doc/41270>.

@article{Caetano1996,

abstract = {A connection on a principal G-bundle may be identified with a smooth group morphism H : GL∞(M) → G, called a holonomy, where GL∞(M) is a group of equivalence classes of loops on the base M. The present article focuses on the kernel of this morphism, which consists of the classes of loops along which parallel transport is trivial. Use is made of a formula expressing the gauge potential as a suitable derivative of the holonomy, allowing a different proof of a theorem of Lewandowski’s, which states that the kernel of the holonomy contains all the information about the corresponding connection. Some remarks are made about nonsmooth holonomies in the context of quantum Yang-Mills theories.},

author = {Caetano, Ana Paula},

journal = {Publicacions Matemàtiques},

keywords = {Kernel; Grupos de holonomia; Gravitación; Teorías Gauge; Teoría cuántica de campos; Grupos de Lie; Conexiones; Espacio de lazos; Morfismos; Teoría del potencial; Geometría diferencial; homotopy; loop spaces; holonomy},

language = {eng},

number = {2},

pages = {373-381},

title = {On the kernel of holonomy.},

url = {http://eudml.org/doc/41270},

volume = {40},

year = {1996},

}

TY - JOUR

AU - Caetano, Ana Paula

TI - On the kernel of holonomy.

JO - Publicacions Matemàtiques

PY - 1996

VL - 40

IS - 2

SP - 373

EP - 381

AB - A connection on a principal G-bundle may be identified with a smooth group morphism H : GL∞(M) → G, called a holonomy, where GL∞(M) is a group of equivalence classes of loops on the base M. The present article focuses on the kernel of this morphism, which consists of the classes of loops along which parallel transport is trivial. Use is made of a formula expressing the gauge potential as a suitable derivative of the holonomy, allowing a different proof of a theorem of Lewandowski’s, which states that the kernel of the holonomy contains all the information about the corresponding connection. Some remarks are made about nonsmooth holonomies in the context of quantum Yang-Mills theories.

LA - eng

KW - Kernel; Grupos de holonomia; Gravitación; Teorías Gauge; Teoría cuántica de campos; Grupos de Lie; Conexiones; Espacio de lazos; Morfismos; Teoría del potencial; Geometría diferencial; homotopy; loop spaces; holonomy

UR - http://eudml.org/doc/41270

ER -

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