Manuscript I-B-VP-0@1 · I-B-VP-0-v1.tex · definition · 8a9d0682

Definition: Distinguished charged Friedrichs ground state

Prescribed geometry, bundle, and spectral state › Massless infrared finiteness · lines 345–358

I-B-VP-0@1#def:state, I-B-VP-0@1#eq:W

The state $ω_{F}$ is the zero-mean, gauge-invariant quasifree spectral Fock state with particle and antiparticle sectors on $L_{β}$ and its conjugate bundle. Its positive-frequency kernel is

W_{β} (t - t^{'}; x, x^{'}) = [\frac{e ^{- i (t - t^{'}) B_{β}}}{2 B _{β}}] (x, x^{'}) = ω_{F} (Φ (X) Φ^{†} (X^{'})) .

Displayed formulas in this passage

I-B-VP-0@1#eq:W · line 350
$W_{β} (t - t^{'}; x, x^{'}) = [\frac{e ^{- i (t - t^{'}) B_{β}}}{2 B _{β}}] (x, x^{'}) = ω_{F} (Φ (X) Φ^{†} (X^{'})) .$

Nearby in this section

lemma: Lemma: Heat kernel and compact-test covariance
section: Massless infrared finiteness