Manuscript X-C-ST@1 · X-C-ST.tex · definition · b679954e

Definition: Coordinate and switch defects

Formal duality and the two defects · lines 1296–1312

X-C-ST@1#def:defects, X-C-ST@1#eq:defects

For arbitrary compact generators in the open slab, define

Θ_{F} [q] = c [q^{'}] - F^{♯} c [q], Σ_{F} [q] = E_{g} [q^{'}] F^{*} - F^{♯} E_{g} [q] .

Write

Θ_{F} = κ θ_{1} + κ^{2} θ_{2}, Σ_{F} = κ S_{1} + κ^{2} S_{2} .

The $θ_{j}$ are tests; the $S_{j}$ are differential operators.

Displayed formulas in this passage

X-C-ST@1#eq:defects · line 1300
$Θ_{F} [q] = c [q^{'}] - F^{♯} c [q], Σ_{F} [q] = E_{g} [q^{'}] F^{*} - F^{♯} E_{g} [q] .$
unlabeled · line 1306
$Θ_{F} = κ θ_{1} + κ^{2} θ_{2}, Σ_{F} = κ S_{1} + κ^{2} S_{2} .$