Manuscript X-F-ST@1 · X-F-ST.tex · section · e71f03ef

Completed tests, counted once

Frozen analytical data and the scalar insertion target › Completed tests, counted once · lines 457–477

X-F-ST@1#eq:completed

Set

c_{1} [l] c_{2} [h, k] d_{1} [l] d_{2} [h, k] = \partial_{μ} (f w^{μ} [l]), = - \partial_{μ} (f (w^{ν} [h] \partial_{ν} w^{μ} [h] - v^{μ} [h, k])) + \frac{1}{2} \partial_{μ} \partial_{ν} (f w^{μ} [h] w^{ν} [h]), = c_{1} [l] - L_{1} [l] E_{m}^{A} f, = c_{2} [h, k] - L_{1} [h] E_{m}^{A} c_{1} [h] - L_{2} [h, k] E_{m}^{A} f + L_{1} [h] E_{m}^{A} L_{1} [h] E_{m}^{A} f .

These are the X-C-ST insertion representatives XCST,XC. They are actual off-shell tests before any quotient is taken.

Displayed formulas in this passage

X-F-ST@1#eq:completed · line 460
$c_{1} [l] c_{2} [h, k] d_{1} [l] d_{2} [h, k] = \partial_{μ} (f w^{μ} [l]), = - \partial_{μ} (f (w^{ν} [h] \partial_{ν} w^{μ} [h] - v^{μ} [h, k])) + \frac{1}{2} \partial_{μ} \partial_{ν} (f w^{μ} [h] w^{ν} [h]), = c_{1} [l] - L_{1} [l] E_{m}^{A} f, = c_{2} [h, k] - L_{1} [h] E_{m}^{A} c_{1} [h] - L_{2} [h, k] E_{m}^{A} f + L_{1} [h] E_{m}^{A} L_{1} [h] E_{m}^{A} f .$