On the Support of Physical Measures in Gauge Theories

Details On the Support of Physical Measures in Gauge Theories On the Support of Physical Measures in Gauge Theories

2001-09-26

arxiv.org/abs/math-ph/0109030v1

Physics

Mathematical Physics

42 pages, LaTeX

Scientific paper

It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of these two measures is given. Finally, the results are extended to more general (e.g. confining) theories. Such a singularity implies, in particular, that the standard method of determining the physical measure via ``exponential of minus the action times kinematical measure'' is not applicable.

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