Communications in Mathematical Physics

, Volume 123, Issue 4, pp 575–616 | Cite as

YM2:Continuum expectations, lattice convergence, and lassos

  • Bruce K. Driver
Article
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Abstract

The two dimensional Yang-Mills theory (YM2) is analyzed in both the continuum and the lattice. In the complete axial gauge the continuum theory may be defined in terms of a Lie algebra valued white noise, and parallel translation may be defined by stochastic differential equations. This machinery is used to compute the expectations of gauge invariant functions of the parallel translation operators along a collection of curvesC. The expectation values are expressed as finite dimensional integrals with densities that are products of the heat kernel on the structure group. The time parameters of the heat kernels are determined by the areas enclosed by the collectionC, and the arguments are determined by the crossing topologies of the curves inC. The expectations for the Wilson lattice models have a similar structure, and from this it follows that in the limit of small lattice spacing the lattice expectations converge to the continuum expectations. It is also shown that the lasso variables advocated by L. Gross [36] exist and are sufficient to generate all the measurable functions on the YM2-measure space.

Keywords

Stochastic Differential Equation Heat Kernel Lasso Invariant Function Translation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Bruce K. Driver
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego, La JollaUSA

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