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A gauge-independent mechanism for confinement and mass gap. I: The general framework. (English) Zbl 1204.81123

Summary: We propose a gauge-independent mechanism for the area-law behavior of Wilson loop expectation values in terms of worldsheets spanning Wilson loops interacting with the spin foams that contribute to the vacuum partition function. The method uses an exact transformation of lattice-regularized Yang-Mills theory that is valid for all couplings. Within this framework, some natural conjectures can be made as to what physical mechanism enforces the confinement property in the continuum (weak coupling) limit. Details for the \(SU(2)\) case in three space-time dimensions are provided in a companion paper.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T25 Quantum field theory on lattices
83C45 Quantization of the gravitational field
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