Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity

Details Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity

2010-03-24

arxiv.org/abs/1003.4591v2

J.Math.Phys.51:103501,2010

Physics

Mathematical Physics

15 pages, 1 figure

Scientific paper

10.1063/1.3496386

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.

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