Manuscript III@2 · III.tex · section · 82dad3e5

An explicit nonzero compact pair

Compact coupled Ward observables › An explicit nonzero compact pair · lines 2242–2255

The pair is genuinely coupled:

\partial_{μ} J^{μ 0} = a^{'} (τ) b (x) \neq \equiv 0.

Neither term is separately invariant under unrestricted compact gauge variations. Its scalar coefficient cannot lie in the adjoint-exact family.

The test solution has nonzero homogeneous scalar data. It is not in a prescription setting $φ$ 's initial data to zero; that prescription is not preserved by all residual gauges.

Displayed formulas in this passage

unlabeled · line 2245
$\partial_{μ} J^{μ 0} = a^{'} (τ) b (x) \neq \equiv 0.$

Nearby in this section

section: An explicit nonzero compact pair
theorem: Theorem: Nontrivial compact coupled quotient observable
figure: Exact zero repair, not every compact Ward pair