In a variety of situations, integrals of products of eigenfunctions have faster decay than smoothness entails. This phenomenon does not appear for abelian or compact groups, since irreducibles are finite-dimensional, so the decomposition of a tensor product of irreducibles is finite. In contrast, for non-compact, nonabelian groups irreducibles are typically infinite-dimensional, and the decompo...

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As an application, the duality breaking for group bundles vs. tensor C*-categories with non-simple unit is discussed in the setting of Nistor-Troitsky gauge-eq...

We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the “isotopic” vector and the stress tensor currents of spins 1 and 2 respectively, we explain this diffe...

In O(3) symmetry electrodynamics the field tensor is governed by a nonAbelian Stokes Theorem, as in any non-Abelian gauge theory. The comments on the B component of this field tensor by Hunter in this Issue address B as if it were a U(1) symmetry field, governed by the ordinary Stokes Theorem, and are therefore sequentially erroneous, because there is a basic misunderstanding of the nature of O...

We consider a Yang–Mills theory in loop space with an affine Lie gauge group. The Chapline–Manton coupling, the coupling between Yang–Mills fields and an abelian antisymmetric tensor field of the second rank via the Chern– Simons term, is systematically derived within the framework of the Yang–Mills theory. The generalized Chapline–Manton couplings, the couplings among nonabelian tensor fields ...