Manuscript XIV-B@1 · XIV-B.tex · section · 53202eaa

Local functionals on and the antibracket

B1: the relative algebra, not a quantum carrier › Local functionals on and the antibracket · lines 509–526

XIV-B@1#eq:antibracket

For $F, G$ functionals of fields and antifields the antibracket is

(F, G) = \int [\frac{δ ^{R} F}{δ Φ ^{A}} \frac{δ ^{L} G}{δ Φ _{A}^{*}} - \frac{δ ^{R} F}{δ Φ _{A}^{*}} \frac{δ ^{L} G}{δ Φ ^{A}}] d^{4} x,

with the left/right Euler derivatives and the sign conventions of HT (Ch. 15). It has parity $∣ F ∣ + ∣ G ∣ + 1$ and ghost number $gh F + gh G + 1$ , and satisfies the graded Jacobi identity HT,GPS,FRBV.

Displayed formulas in this passage

XIV-B@1#eq:antibracket · line 512
$(F, G) = \int [\frac{δ ^{R} F}{δ Φ ^{A}} \frac{δ ^{L} G}{δ Φ _{A}^{*}} - \frac{δ ^{R} F}{δ Φ _{A}^{*}} \frac{δ ^{L} G}{δ Φ ^{A}}] d^{4} x,$

Nearby in this section

definition: Definition: The algebra
lemma: Lemma: Finiteness and locality