Quantum Yang-Mills Theory, section 6.5 (Yang-Mills Theory: Wilson's lattice approach)

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Wilson suggested a different approach based on approximating continuum space-time by a lattice, on which he defined a gauge-invariant action [48]. With a compact gauge group and a compactified space-time, the lattice approximation reduces the functional integration to a finite-dimensional integral. One must then verify the existence of limits of appropriate expectations of gauge-invariant observables as the lattice spacing tends to zero and as the volume tends to infinity.

Ссылаются нормы: WilsonLatticeDirect, WilsonLatticeProof, WilsonLatticeWellDefinedClaim, WilsonSource, lattice_well_defined_for, wilson-proves-lattice-well-defined

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Reflection positivity holds for the Wilson approximation [36], a major advantage; few methods exist to recover reflection positivity in case it is lost through regularization -- such as with dimensional regularization, Pauli-Villiars regularization, and many other methods. Establishing a quantum mechanical Hilbert space is part of the solution to this Millennium problem.

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[48] K. G. Wilson, Quarks and strings on a lattice, in New Phenomena In Subnuclear Physics, Proceedings of the 1975 Erice School, A. Zichichi, ed., Plenum Press, New York, 1977.