Mourao JM, Thiemann T, Velhinho J (1999)

**Publication Status:** Published

**Publication Type:** Journal article

**Publication year:** 1999

**Publisher:** AMER INST PHYSICS

**Book Volume:** 40

**Pages Range:** 2337-2353

**Journal Issue:** 5

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. In particular 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. (C) 1999 American Institute of Physics. [S0022-2488(99)00404-1].

José Manuel Mourao
Chair for Theoretical Physics III (Quantum Gravity)
Thomas Thiemann
Chair for Theoretical Physics III (Quantum Gravity)

**APA:**

Mourao, J.M., Thiemann, T., & Velhinho, J. (1999). Physical properties of quantum field theory measures. *Journal of Mathematical Physics*, *40*(5), 2337-2353.

**MLA:**

Mourao, José Manuel, Thomas Thiemann, and Jose Velhinho. "Physical properties of quantum field theory measures." *Journal of Mathematical Physics* 40.5 (1999): 2337-2353.

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