ar X iv : g r - qc / 0 70 20 73 v 1 13 F eb 2 00 7 Holonomy Transformation in the FRW Metric
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چکیده
In the loop space formalism for gauge theories the fields depend more on the paths rather than on spacetime points. The fundamental quantity that arises from this path-dependent approach is the non-integrable phase factor that represents a gauge field more adequately than the field strength does. In this approach, electromagnetism, for example, is a gauge-invariant manifestation of the non-integrable phase factor which gives the exact description of the theory, differently from the field strength and the integral of the potential. As another example of the path-dependent formalism we can cite some aspects concerning phases of gauge fields and confinement of quarks [1]. The extension of the loop space formalism to the theory of gravity was firstly considered by Mandelstam [2] who established several equations involving loop variables, and also by Yang [3], Voronov and Makeenko [4]. Mathematically speaking, holonomy is a matrix that represents the parallel transport of vectors, spinors, tensors, etc. This matrix provides information on the curvature and topology of a given manifold. The holonomy matrix can be written as
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تاریخ انتشار 2007