Invariance properties of induced Fock measures for U(1) holonomies

We study invariance properties of the measures in the space of generalized U(1) connections associated to Varadarajan's r-Fock representations.Comment: Shorter introduction and review sections. New discussion section. To appear in Comm. Math. Phy

Some properties of generalized connections in quantum gravity

The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous description of the gauge-invariant quantum configuration space of Ashtekar and Isham. We present a description of the groupoid approach which brings the gauge-invariant degrees of freedom to the foreground, thus making the action of the gauge group more transparent.Comment: LaTeX, 11 pages. Submitted to the on-line proceedings of the Ninth Marcel Grossmann Meeting (Rome, July 2000). Talk based on hep-th/001120

Functorial Aspects of the Space of Generalized Connections

We give a description of the category structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.Comment: 7 pages. To appear in Proceedings of the Lusofona Workshop on Quantum Gravity and Noncommutative Geometry, Lisbon, July 200

Comments on a Full Quantization of the Torus

Gotay showed that a representation of the whole Poisson algebra of the torus given by geometric quantization is irreducible with respect to the most natural overcomplete set of observables. We study this representation and argue that it cannot be considered as physically acceptable. In particular, classically bounded observables are quantized by operators with unbounded spectrum. Effectively, the latter amounts to lifting the constraints that compactify both directions in the torus.Comment: 10 pages. New "Discussion" section. References added. To appear in IJMP

Physical Properties of Quantum Field Theory Measures

Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. We prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.Comment: 24 pages, LaTeX, added proof for section 4.2, added reference

Comments on the kinematical structure of loop quantum cosmology

We comment on the presence of spurious observables and on a subtle violation of irreducibility in loop quantum cosmology.Comment: 7 page