Manuscript VI@1 · VI.tex · section · b5b60afb

The named gauge group

Action, signs, background, and coefficient domain › The named gauge group · lines 506–528

VI@1#eq:formal-pullback

Let

g_{T} = C_{c}^{\infty} ((0, T) \times R^{3}; T M) .

Gauge transformations are formal pullbacks

F_{ξ, ζ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) mod κ^{3}, ξ, ζ \in g_{T} .

The corresponding transformations are the identity near the initial surface. They form a group of formal second-order transformations under composition. Closure follows from the Baker–Campbell–Hausdorff formula and closure of $g_{T}$ under the Lie bracket.

The use of compact support is a convenient sufficient condition. No residual-wave gauge group is substituted for this group.

Displayed formulas in this passage

VI@1#eq:formal-pullback · line 513
$F_{ξ, ζ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) mod κ^{3}, ξ, ζ \in g_{T} .$
unlabeled · line 509
$g_{T} = C_{c}^{\infty} ((0, T) \times R^{3}; T M) .$

The named gauge group

Displayed formulas in this passage

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