Manuscript Psy02-A@1 · Psy02-A.tex · section · d92ce402

Model and punctured response

A separate normalization-independent response benchmark › Model and punctured response · lines 1564–1590

Psy02-A@1#eq:response-definition

Work on four-dimensional Minkowski space, with $c = 1$ , and write

z = (t, x), s (z) = t^{2} - \abs x^{2} .

Use a free massless scalar vacuum with

ω_{0} (φ (x) φ (y)) = ℏ W (x - y), W (z) = - \frac{1}{4 π ^{2}} (s (z) - i 0 t)^{- 1} .

Let

Q (x) =: φ (x)^{2} :

be vacuum-calibrated. Fix the source sign so that the first retarded response is

R^{\circ} (z) = \frac{i}{ℏ} Θ (t) ω_{0} ([Q (z), Q (0)]), z \neq = 0.

Displayed formulas in this passage

unlabeled · line 1567
$z = (t, x), s (z) = t^{2} - \abs x^{2} .$
unlabeled · line 1571
$ω_{0} (φ (x) φ (y)) = ℏ W (x - y), W (z) = - \frac{1}{4 π ^{2}} (s (z) - i 0 t)^{- 1} .$
unlabeled · line 1577
$Q (x) =: φ (x)^{2} :$
Psy02-A@1#eq:response-definition · line 1582
$R^{\circ} (z) = \frac{i}{ℏ} Θ (t) ω_{0} ([Q (z), Q (0)]), z \neq = 0.$