Abstract
Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator [Formula: see text] built from the Laplacian and from a first-order differential operator. The operator [Formula: see text] is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of [Formula: see text] are evaluated as a first step towards the more difficult problems of quantized Yang–Mills theory.
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