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

What belongs to the interactions

Second-order retarded bookkeeping and the missing quantum step › What belongs to the interactions · lines 1894–1920

VI@1#eq:V2matter

With $γ = η + κh$ , the classical interaction contains

V_{1} = V_{1}^{grav} + V_{1}^{m}, V_{2} = V_{2}^{grav} + V_{2}^{m} .

The gravity terms are the cubic and quartic coefficients of the Einstein–Hilbert density. The matter terms are

V_{1}^{m} V_{2}^{m} = \frac{1}{2} \int h^{μν} T_{μν} (η, φ) d^{4} x, = - \frac{1}{2} \int (C_{h}^{μν} \partial_{μ} φ \partial_{ν} φ + e_{h} m^{2} φ^{2}) d^{4} x .

A gauge-fixed quantum construction additionally requires its ghost and gauge-fixing interactions.

Multiplying a chosen local density by $g$ , or assigning powers or independent copies of switches to different orders, is additional data. These choices cannot be left implicit in a finite counterterm classification.

Displayed formulas in this passage

VI@1#eq:V2matter · line 1904
$V_{1}^{m} V_{2}^{m} = \frac{1}{2} \int h^{μν} T_{μν} (η, φ) d^{4} x, = - \frac{1}{2} \int (C_{h}^{μν} \partial_{μ} φ \partial_{ν} φ + e_{h} m^{2} φ^{2}) d^{4} x .$
unlabeled · line 1897
$V_{1} = V_{1}^{grav} + V_{1}^{m}, V_{2} = V_{2}^{grav} + V_{2}^{m} .$