Robustness of the vacuum wave function and other matters for Yang-Mills theory

In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the ($2+1$)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of ($2+1$)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to ($3+1$)-dimensional Yang-Mills theory).