Manuscript XIV-C@1 · XIV-C.tex · section · a34d13df

Definitions used by the branch display

J1: copied branches, line orders, and collision inventory › Definitions used by the branch display · lines 613–658

Write

X = X_{1} [γ], p = p_{1} [γ; ϕ], \int_{f} A = \int f A d^{4} x,

where

X_{1}^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]),

p_{1} [r; ϕ] = - E_{m}^{R} [\partial_{μ} (g a_{1}^{μν} [r] \partial_{ν} ϕ) + m^{2} g b_{1} [r] ϕ] .

The density coefficients are

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

b_{2} [γ] = \frac{1}{8} (tr_{η} γ)^{2} - \frac{1}{4} γ_{α β} γ^{α β},

a_{2}^{μν} [γ] = γ^{μ}_{α} γ^{α ν} - \frac{1}{2} (tr_{η} γ) γ^{μν} + b_{2} [γ] η^{μν} .

Put

U_{σ}_{ε} [γ] q = \partial_{α} (σ_{ε} a_{1}^{α β} [γ] \partial_{β} q),

V_{2, g} [γ, 0] ϕ = \partial_{μ} (g a_{2}^{μν} [γ] \partial_{ν} ϕ) + m^{2} g b_{2} [γ] ϕ .

Displayed formulas in this passage

unlabeled · line 616
$X = X_{1} [γ], p = p_{1} [γ; ϕ], \int_{f} A = \int f A d^{4} x,$
unlabeled · line 621
$X_{1}^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]),$
unlabeled · line 625
$p_{1} [r; ϕ] = - E_{m}^{R} [\partial_{μ} (g a_{1}^{μν} [r] \partial_{ν} ϕ) + m^{2} g b_{1} [r] ϕ] .$
unlabeled · line 632
$a_{1}^{μν} [r] = \frac{1}{2} η^{μν} tr_{η} r - r^{μν}, b_{1} [r] = \frac{1}{2} tr_{η} r,$
unlabeled · line 637
$b_{2} [γ] = \frac{1}{8} (tr_{η} γ)^{2} - \frac{1}{4} γ_{α β} γ^{α β},$
unlabeled · line 642
$a_{2}^{μν} [γ] = γ^{μ}_{α} γ^{α ν} - \frac{1}{2} (tr_{η} γ) γ^{μν} + b_{2} [γ] η^{μν} .$
unlabeled · line 649
$U_{σ}_{ε} [γ] q = \partial_{α} (σ_{ε} a_{1}^{α β} [γ] \partial_{β} q),$
unlabeled · line 653
$V_{2, g} [γ, 0] ϕ = \partial_{μ} (g a_{2}^{μν} [γ] \partial_{ν} ϕ) + m^{2} g b_{2} [γ] ϕ .$