Manuscript X-H-ST@1 · X-H-ST.tex · section · 943aa27e

Local variational meaning

Stage B: an explicit relative classical master action › Local variational meaning · lines 597–620

Let a local Lagrangian mean a horizontal four-form modulo a horizontal divergence:

[L] \in Ω_{H}^{4} (U) / d_{H} Ω_{H}^{3} (U) .

Euler differentiation annihilates divergences. Generalized actions act on compactly supported local functionals by their local Euler derivatives.

We use the algebra generated by compact local functionals under ordinary multiplication. It is a multilocal algebra, denoted $F_{ml} (U)$ ; products of two single integrals are not falsely declared to be single local integrals. The classical variational bracket is defined on this algebra with its usual integration-by-parts identifications FRBV.

No time-ordered product, Wick extension, or BV Laplacian is required for this classical operation.

Displayed formulas in this passage

unlabeled · line 601
$[L] \in Ω_{H}^{4} (U) / d_{H} Ω_{H}^{3} (U) .$