Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

Free-limit statements with the tadpole retained

The retained classical interface and its recovery › Free-limit statements with the tadpole retained · lines 598–625

For clarity, define

(P_{tr} r)_{μν} = r_{μν} - \frac{1}{2} η_{μν} tr_{η} r, (C r)^{μ} = \partial_{ν} (P_{tr} r)^{ν μ} .

The free normalization is

A = \frac{1}{2} G_{lin}, A K = 0, C^{*} = - \frac{1}{2} P_{tr} K, C K = □,

A + \frac{1}{2} C^{*} C = P_{gr} = - \frac{1}{4} P_{tr} □ .

The free action is

I_{free} = \frac{1}{2} ⟨ r, A r ⟩ - \frac{1}{2} ⟨ ϕ, (□ + m^{2}) ϕ ⟩ + \int (b \cdot C r - b^{2} - c ˉ \cdot □ c) d^{4} x .

Displayed formulas in this passage

unlabeled · line 601
$(P_{tr} r)_{μν} = r_{μν} - \frac{1}{2} η_{μν} tr_{η} r, (C r)^{μ} = \partial_{ν} (P_{tr} r)^{ν μ} .$
unlabeled · line 608
$A = \frac{1}{2} G_{lin}, A K = 0, C^{*} = - \frac{1}{2} P_{tr} K, C K = □,$
unlabeled · line 614
$A + \frac{1}{2} C^{*} C = P_{gr} = - \frac{1}{4} P_{tr} □ .$
unlabeled · line 619
$I_{free} = \frac{1}{2} ⟨ r, A r ⟩ - \frac{1}{2} ⟨ ϕ, (□ + m^{2}) ϕ ⟩ + \int (b \cdot C r - b^{2} - c ˉ \cdot □ c) d^{4} x .$