Quantum Yang-Mills on the two-sphere |
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Authors: | Dana S Fine |
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Institution: | (1) Department of Mathematics, Southeastern Massachusetts University, 02747 North Dartmouth, MA, USA |
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Abstract: | We obtain the quantum expectations of gauge-invariant functions of the connection on a principalG=SU(N) bundle overS
2. We show that the spaceA/g
m of connections modulo gauge transformations which are the identity at one point is itself a principal bundle over G, based loops in the symmetry group. The fiber inA/g
m is an affine linear space. Quantum expectations are iterated path integrals first over this fiber then over G, each with respect to the push-forward toA/g
m of the measure s-S(A)
DA.S(A) denotes the Yang-Mills action onA. There is a global section ofA/g
m on which the first integral is a Gaussian. The resulting measure on G is the conditional Wiener measure. We explicitly compute the expectations of a special class of Wilson loops. |
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Keywords: | |
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