Manuscript XIV-G@1 · XIV-G.tex · input · 791c6644

Input statement: Completion, slots, and roots

G0: copied inputs and the unchanged stop › Earlier analytic handoffs · lines 676–710

XIV-G@1#input:XIIE

The inherited formulas are

Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D}, r_{D} = - u_{D} = P E_{0}^{R} J_{D},

r_{g} [ϕ] = - \frac{1}{2} P E_{0}^{R} (g T_{0} [ϕ]),

X^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]), p [r; ψ] = - E_{m}^{R} (V_{1, g} [r] ψ),

where

a_{1}^{μν} [r] = \frac{1}{2} η^{μν} tr_{η} r - r^{μν}, b_{1} [r] = \frac{1}{2} tr_{η} r,

V_{1, g} [r] ψ = \partial_{μ} (g a_{1}^{μν} [r] \partial_{ν} ψ) + m^{2} g b_{1} [r] ψ .

The roots satisfy

A_{1} [f, g] (r; ϕ) = \int α_{f, g} [ϕ] \cdot r d^{4} x, β_{f, g} [ϕ] = - E_{0}^{A} (P α_{f, g} [ϕ]) .

The completion and filled-slot kernels are admitted tree kernels XIIE.

Displayed formulas in this passage

unlabeled · line 679
$Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D}, r_{D} = - u_{D} = P E_{0}^{R} J_{D},$
unlabeled · line 683
$r_{g} [ϕ] = - \frac{1}{2} P E_{0}^{R} (g T_{0} [ϕ]),$
unlabeled · line 686
$X^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]), p [r; ψ] = - E_{m}^{R} (V_{1, g} [r] ψ),$
unlabeled · line 692
$a_{1}^{μν} [r] = \frac{1}{2} η^{μν} tr_{η} r - r^{μν}, b_{1} [r] = \frac{1}{2} tr_{η} r,$
unlabeled · line 697
$V_{1, g} [r] ψ = \partial_{μ} (g a_{1}^{μν} [r] \partial_{ν} ψ) + m^{2} g b_{1} [r] ψ .$
unlabeled · line 703
$A_{1} [f, g] (r; ϕ) = \int α_{f, g} [ϕ] \cdot r d^{4} x, β_{f, g} [ϕ] = - E_{0}^{A} (P α_{f, g} [ϕ]) .$