Communications in Mathematical Physics

, Volume 134, Issue 2, pp 273–292 | Cite as

Quantum Yang-Mills on the two-sphere

  • Dana S. Fine


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.


Symmetry Group Linear Space Gauge Transformation Special Class Wilson Loop 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Dana S. Fine
    • 1
  1. 1.Department of MathematicsSoutheastern Massachusetts UniversityNorth DartmouthUSA

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