Manuscript XX-E@1 · XX-E.tex · section · cf7a8f40

The central-second-jet issue

Why the free input does not supply a quantum Ward operation › The central-second-jet issue · lines 801–826

XX-D treats $ζ$ as prescribed classical parameters in its free Wick construction. That choice is legitimate for a family of insertions. It does not automatically define a quantum gauge transformation of those parameters inside a fixed algebra.

Let

Z_{g} = (z, g)_{0}, M_{a} = (ζ, a)_{0}

for compact tests. In the central-parameter extension, all $M_{a}$ are central, whereas

[Z_{g}, Z_{b}]_{⋆_{W}} = i ℏ E_{B} (g, b) id .

The classical transformation (eq:jetgauge) would give

V_{ξ} Z_{g} = (K ξ, g)_{0} id, V_{ξ} M_{a} = 2 Z_{A_{ξ}^{†} a} .

Displayed formulas in this passage

unlabeled · line 811
$Z_{g} = (z, g)_{0}, M_{a} = (ζ, a)_{0}$
unlabeled · line 816
$[Z_{g}, Z_{b}]_{⋆_{W}} = i ℏ E_{B} (g, b) id .$
unlabeled · line 822
$V_{ξ} Z_{g} = (K ξ, g)_{0} id, V_{ξ} M_{a} = 2 Z_{A_{ξ}^{†} a} .$

The central-second-jet issue

Displayed formulas in this passage

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