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

Definition: Renormalized one-point current

Noether normalization and renormalized current › Point splitting and the complex first jet · lines 510–528

I-B-VP-0@1#def:current, I-B-VP-0@1#eq:currentdefinition

In a local parallel frame, define

J_{μ} := ⟨ J_{μ} ⟩_{ren} = i [(\partial_{μ} - \partial_{μ^{'}}) H_{β} (X, X^{'})],

where brackets mean coincidence and primed covectors are parallel transported before identification.

Equivalently, one may use the locally regularized symmetrized two-point function with coefficient $i /2$ . For spatial components the same formula is obtained from $H_{E, β}$ at equal Euclidean times.

Displayed formulas in this passage

I-B-VP-0@1#eq:currentdefinition · line 513
$J_{μ} := ⟨ J_{μ} ⟩_{ren} = i [(\partial_{μ} - \partial_{μ^{'}}) H_{β} (X, X^{'})],$

Nearby in this section

section: Point splitting and the complex first jet
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