Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

A fixed insertion and contact prescription

The finite local-Ward certificate › A fixed insertion and contact prescription · lines 870–899

Oai282-A@1#eq:divdefect, Oai282-A@1#eq:tracedefect, Oai282-A@1#eq:contactdefect, Oai282-A@1#eq:wardresidual

This contract is not the full :framework of Family 282. It neither reconstructs $L$ nor asserts all physical mixed products.

Define the divergence, trace, and contact-matching defects:

E^{r}_{ν} E^{r}_{tr} K^{r}_{X} = \partial^{μ} T^{r}_{μν} - P^{r}_{ν}, = η^{μν} T^{r}_{μν} - □_{x} L^{r} - S^{r}, = X^{ν} P^{r}_{ν} + σ_{X} S^{r} - C^{r}_{X} .

The finite Ward residual is

W_{r aj} = [\partial^{μ} (X_{a}^{ν} t^{r}_{μν}) - C^{r}_{X_{a}}] (f_{r aj}) .

Displayed formulas in this passage

Oai282-A@1#eq:divdefect · line 877
$E^{r}_{ν} E^{r}_{tr} K^{r}_{X} = \partial^{μ} T^{r}_{μν} - P^{r}_{ν}, = η^{μν} T^{r}_{μν} - □_{x} L^{r} - S^{r}, = X^{ν} P^{r}_{ν} + σ_{X} S^{r} - C^{r}_{X} .$
Oai282-A@1#eq:tracedefect · line 877
$E^{r}_{ν} E^{r}_{tr} K^{r}_{X} = \partial^{μ} T^{r}_{μν} - P^{r}_{ν}, = η^{μν} T^{r}_{μν} - □_{x} L^{r} - S^{r}, = X^{ν} P^{r}_{ν} + σ_{X} S^{r} - C^{r}_{X} .$
Oai282-A@1#eq:contactdefect · line 877
$E^{r}_{ν} E^{r}_{tr} K^{r}_{X} = \partial^{μ} T^{r}_{μν} - P^{r}_{ν}, = η^{μν} T^{r}_{μν} - □_{x} L^{r} - S^{r}, = X^{ν} P^{r}_{ν} + σ_{X} S^{r} - C^{r}_{X} .$
Oai282-A@1#eq:wardresidual · line 891
$W_{r aj} = [\partial^{μ} (X_{a}^{ν} t^{r}_{μν}) - C^{r}_{X_{a}}] (f_{r aj}) .$