Holonomy of a principal composite bundle connection, non-Abelian geometric phases, and gauge theory of gravity
- Institut UTINAM, CNRS UMR 6213, Observatoire de Besancon, Universite de Franche-Comte, 41bis Avenue de l'Observatoire, BP1615, 25010 Besancon Cedex (France)
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
- OSTI ID:
- 21476578
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 10; Other Information: DOI: 10.1063/1.3496386; (c) 2010 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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