Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 006, 8 pages      arXiv:1410.7736

Local Properties of Measures in Quantum Field Theory and Cosmology

José M. Velhinho
Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D'Ávila e Bolama, 6201-001 Covilhã, Portugal

Received October 30, 2014, in final form January 14, 2015; Published online January 17, 2015

We show that measure theoretical results concerning the Ashtekar-Lewandowski measure in the space of generalized connections have direct analogues in the context of the Bohr compactification of the line and associated Haar measure. We present also a characterization of the support of the measure associated with the canonical quantization of the free massive scalar field, following closely well known analogous results concerning the Euclidean path integral measure.

Key words: canonical quantization; scalar field; loop cosmology; support of the measure.

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