Quantum Yang-Mills on the two-sphere

1990
20 pages
Published in:
  • Commun.Math.Phys. 134 (1990) 273-292

Citations per year

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Abstract: (Springer)
We obtain the quantum expectations of gauge-invariant functions of the connection on a principalG=SU(N) bundle overS2. We show that the spaceA/gm of connections modulo gauge transformations which are the identity at one point is itself a principal bundle over ΩG, based loops in the symmetry group. The fiber inA/gm is an affine linear space. Quantum expectations are iterated path integrals first over this fiber then over ΩG, each with respect to the push-forward toA/gm of the measure s-S(A)DA.S(A) denotes the Yang-Mills action onA. There is a global section ofA/gm on which the first integral is a Gaussian. The resulting measure on ΩG is the conditional Wiener measure. We explicitly compute the expectations of a special class of Wilson loops.
  • gauge field theory: SU(N)
  • dimension: 2
  • space-time: sphere
  • fibre bundle
  • path integral
  • Wilson loop
  • mathematical methods
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