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Titolo:
Loop and path spaces and four-dimensional BF theories: Connections, holonomies and observables
Autore:
Cattaneo, AS; Cotta-Ramusino, P; Rinaldi, M;
Indirizzi:
Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy Univ Milan Milan Italy I-20133 ipartimento Matemat, I-20133 Milan, Italy Ist Nazl Fis Nucl, Sez Milano, I-20133 Milan, Italy Ist Nazl Fis Nucl Milan Italy I-20133 , Sez Milano, I-20133 Milan, Italy Univ Trieste, Dipartimento Matemat, I-34127 Trieste, Italy Univ Trieste Trieste Italy I-34127 mento Matemat, I-34127 Trieste, Italy
Titolo Testata:
COMMUNICATIONS IN MATHEMATICAL PHYSICS
fascicolo: 3, volume: 204, anno: 1999,
pagine: 493 - 524
SICI:
0010-3616(199908)204:3<493:LAPSAF>2.0.ZU;2-6
Fonte:
ISI
Lingua:
ENG
Soggetto:
GAUGE-THEORY; QUARK CONFINEMENT; EMBEDDED SURFACES; FIELD-STRENGTH; QCD; CONSTRAINTS; FORMULATION; INVARIANTS; SYSTEMS; BOSON;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
33
Recensione:
Indirizzi per estratti:
Indirizzo: Cattaneo, AS Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy Univ Milan Via Saldini 50 Milan Italy I-20133 3 Milan, Italy
Citazione:
A.S. Cattaneo et al., "Loop and path spaces and four-dimensional BF theories: Connections, holonomies and observables", COMM MATH P, 204(3), 1999, pp. 493-524

Abstract

We study the differential geometry of principal G-bundles whose base spaceis the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A, B), where A is a connection for a fixed principal bundle P(M, G) and B is a 2-form on M, The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A, B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non-topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.

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Documento generato il 05/04/20 alle ore 19:00:46