Manuscript X-G@1 · X-G.tex · section · 01566e14

The switched scalar action: an evaluated breaking

The switched scalar action: an evaluated breaking · lines 941–971

Consider the natural reference action

S_{ref} = S_{EH} + S_{g}^{sc} + s Ψ_{q ˉ},

where

S_{g}^{sc} = \int ((1 - g) L_{η} [ϕ] + g L_{q} [q, ϕ]) d^{4} x,

L_{q} = \frac{1}{2} - q (q^{μν} \partial_{μ} ϕ \partial_{ν} ϕ - m^{2} ϕ^{2}) .

This action is used to evaluate its natural gauge variation. Its Euler equation is not identified with X-F's post-variation source-switching prescription.

Put

T_{0}^{μν} = \partial^{μ} ϕ \partial^{ν} ϕ - η^{μν} L_{η}, \partial_{μ} T_{0}^{μ}_{ν} = (P_{m} ϕ) \partial_{ν} ϕ .

Displayed formulas in this passage

unlabeled · line 945
$S_{ref} = S_{EH} + S_{g}^{sc} + s Ψ_{q ˉ},$
unlabeled · line 950
$S_{g}^{sc} = \int ((1 - g) L_{η} [ϕ] + g L_{q} [q, ϕ]) d^{4} x,$
unlabeled · line 954
$L_{q} = \frac{1}{2} - q (q^{μν} \partial_{μ} ϕ \partial_{ν} ϕ - m^{2} ϕ^{2}) .$
unlabeled · line 964
$T_{0}^{μν} = \partial^{μ} ϕ \partial^{ν} ϕ - η^{μν} L_{η}, \partial_{μ} T_{0}^{μ}_{ν} = (P_{m} ϕ) \partial_{ν} ϕ .$

The switched scalar action: an evaluated breaking

Displayed formulas in this passage

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