Manuscript I-B-VP-1@1 · I-B-VP-1-v1.tex · definition · 6d700be9

Definition: Prescribed Ward representative

The completion, regular data, and Ward prescription › Which Ward identities are extended? · lines 385–413

I-B-VP-1@1#def:Ward, I-B-VP-1@1#eq:Ward, I-B-VP-1@1#eq:I, I-B-VP-1@1#eq:Iblocks

For the stationary distributions considered here, use

D_{ν} T := \partial_{μ} T^{μ}_{ν}, d J := \partial_{μ} J^{μ}, t T := T^{μ}_{μ} .

For a stationary scalar distribution $G$ , define the smooth reference improvement

I [G]^{μ}_{ν} = δ^{μ}_{ν} □_{g ˉ} G - \partial ˉ^{μ} \partial_{ν} G .

In the present translation-invariant sector,

I [G]^{A}_{B} = δ^{A}_{B} Δ G, I [G]^{i}_{j} = - K_{ij} G, I [G]^{A}_{i} = I [G]^{i}_{A} = 0.

Displayed formulas in this passage

I-B-VP-1@1#eq:Ward · line 388
$D_{ν} T := \partial_{μ} T^{μ}_{ν}, d J := \partial_{μ} J^{μ}, t T := T^{μ}_{μ} .$
I-B-VP-1@1#eq:I · line 398
$I [G]^{μ}_{ν} = δ^{μ}_{ν} □_{g ˉ} G - \partial ˉ^{μ} \partial_{ν} G .$
I-B-VP-1@1#eq:Iblocks · line 405
$I [G]^{A}_{B} = δ^{A}_{B} Δ G, I [G]^{i}_{j} = - K_{ij} G, I [G]^{A}_{i} = I [G]^{i}_{A} = 0.$