Convergence of the Four Dimensional U(1) Lattice Gauge Theory to Its Continuum Limit |
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ACCL Appendix approach to Yang-Mills BCCB cluster property Comm compact support connection form continuous function convergence convex function correlation inequalities cos(m cos(m.w countable number countable set coupling constant defined Definition denotes differential forms dimensional Lebesque measure Dobrushin's uniqueness theorem dw(p dx(t equation estimate exists extreme Gibbs field strength Field Theory finite range finite support free Euclidean functions f Furthermore gauge invariant Gross Hence informal description informal expression integral interaction potential J,ja k-cells k-form lattice approximation lattice gauge theories Lemma Let h Math Michigan preprint non-abelian normalization constant notation o-algebra phase cell approach Phys positively oriented probability measure proof of Theorem Proposition 4.4.1 quantum fields quantum mechanical Remark renormalized sup-norm tangent functional test 1-form thermodynamic limit translation and 90°-rotation translation invariant translation invariant Gibbs Wilson-like energy function Wilson-loop variables Yang-Mills theory zero