Physical Properties of Quantum Field Theory Measures

Details Physical Properties of Quantum Field Theory Measures Physical Properties of Quantum Field Theory Measures

1997-11-18

arxiv.org/abs/hep-th/9711139v2

J.Math.Phys. 40 (1999) 2337-2353

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, LaTeX, added proof for section 4.2, added references

Scientific paper

10.1063/1.532868

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.

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