Manuscript I-B-VP-0@1 · I-B-VP-0-v1.tex · section · 8a9d0682

Point splitting and the complex first jet

Noether normalization and renormalized current › Point splitting and the complex first jet · lines 528–539

At spacelike-separated endpoints the fields commute, so

i (\partial_{μ} - \partial_{μ^{'}}) ω_{F} (Φ (X) Φ^{†} (X^{'}))

has exactly the ordering in (eq:classicalcurrent) after coincidence. The Hadamard subtraction extends this to the local definition (eq:currentdefinition). The difference of endpoint derivatives is essential.

Displayed formulas in this passage

unlabeled · line 531
$i (\partial_{μ} - \partial_{μ^{'}}) ω_{F} (Φ (X) Φ^{†} (X^{'}))$

Nearby in this section

definition: Definition: Renormalized one-point current
remark: Remark: Do not replace the kernel by its real part
section: Point splitting and the complex first jet
assumption: Assumption: Renormalization class
proposition: Proposition: Well-definedness, gauge invariance, and conservation
remark: Remark: A current-specific ambiguity statement