Manuscript I-B-VP@3 · I-B-VP-v3.tex · definition · 93c04eb4

Definition: Distinguished spectral state

Friedrichs heat kernel and the massless state · lines 601–620

I-B-VP@3#def:state

For a nonnegative spatial extension whose compact tests belong to $dom (B^{- 1/4})$ , define

K_{B} f = \int_{R} e^{i t B} (2 B)^{- 1/2} f (t) d t,

and the positive-frequency kernel

W_{B} (t - t^{'}; x, x^{'}) = [\frac{e ^{- i (t - t^{'}) B}}{2 B}] (x, x^{'}) .

The zero-mean quasifree spectral Fock state has smeared covariance $⟨ K_{B} f, K_{B} g ⟩$ .

For a complex field the particle and antiparticle constructions use $B$ and its conjugate extension. Charge-changing two-point functions vanish.

Displayed formulas in this passage

unlabeled · line 605
$K_{B} f = \int_{R} e^{i t B} (2 B)^{- 1/2} f (t) d t,$
unlabeled · line 610
$W_{B} (t - t^{'}; x, x^{'}) = [\frac{e ^{- i (t - t^{'}) B}}{2 B}] (x, x^{'}) .$