Definition: The single normalized map

For the specified representative $F_c$, define

The notation $-⟨c,{{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{R}}{\mathsf{L}}_{1,g}[h]\hat{\varphi }⟩$ means this transposed expression. It does not mean applying an inverse to an unsmeared quantum field without first defining its test action.