Explicit evaluation of group-invariant measure as by-product of path integration over Yang–Mills fields

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Abstract
A method is presented for explicitly evaluating the invariant measure over a Lie group, for any parametrization in which a generic group element is written as a product of exponentials of elements of the Lie algebra. The measure is expressed as a transition amplitude associated with the quantum mechanical evolution operator of the ‘‘ghost fields’’ which appear in the path integral over Yang–Mills fields. As an illustration of the method, the measure is evaluated in two cases: (i) in canonical coordinates, for an arbitrary Lie group which admits them; (ii) in terms of Euler angles, for the group of rotations in three-dimensional space.

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