Manuscript Em06-A@1 · Em06-A-v1.tex · section · ee9923c6

One-particle map and scalar preparation

The quantum family is constructed, not inferred › One-particle map and scalar preparation · lines 567–583

Em06-A@1#eq:k

Let

h = L^{2} (R^{3}, d^{3} p), ⟨ v, z ⟩ = \int_{R^{3}} v (p) z (p) d^{3} p, ω_{p} = ∣ p ∣^{2} + m^{2} .

The inner product is linear in its second argument. For a real compact smooth scalar test $F$ , define

k_{F} (p) = \frac{1}{( 2 π ) ^{3/2} 2 ω _{p}} \int_{M} F (t, x) e^{i ω_{p} t - i p \cdot x} d t d^{3} x .

Displayed formulas in this passage

Em06-A@1#eq:k · line 577
$k_{F} (p) = \frac{1}{( 2 π ) ^{3/2} 2 ω _{p}} \int_{M} F (t, x) e^{i ω_{p} t - i p \cdot x} d t d^{3} x .$
unlabeled · line 570
$h = L^{2} (R^{3}, d^{3} p), ⟨ v, z ⟩ = \int_{R^{3}} v (p) z (p) d^{3} p, ω_{p} = ∣ p ∣^{2} + m^{2} .$