On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the classical configuration space of Yang-Mills theories (i.e. the moduli space of connections) is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices. These results are then used to prove that the classical configuration space is contained in a zero measure subset of this extension with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure. Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the ``extended" configuration space.

gauge field theory: Yang-Mills
phase space: measure
coset space
topology
invariance: diffeomorphism
mathematical methods

References(3)

Figures(0)

Representations of the holonomy algebras of gravity and nonAbelian gauge theories

Abhay Ashtekar
(
- Syracuse U. and
- Imperial Coll., London
)
,
C.J. Isham
(
- Imperial Coll., London
)

- Class.Quant.Grav. 9 (1992) 1433-1468
•
e-Print:
- hep-th/9202053
•
DOI:
- 10.1088/0264-9381/9/6/004

Diffeomorphism invariant generalized measures on the space of connections modulo gauge transformations

John C. Baez
(
- UC, Riverside
)

- ,
- In *Manhattan 1993, Proceedings, Quantum topology* 21-43, and Preprint - Baez, J.C. (93/05,rec.May) 23 p
•
e-Print:
- hep-th/9305045

Comment on a paper of Ashtekar and Isham

A.D. Rendall
(
- Syracuse U.
)

- Class.Quant.Grav. 10 (1993) 605-608
•
DOI:
- 10.1088/0264-9381/10/3/019