Manuscript Em03-F@1 · Em03-F-v1.tex · section · 0d4d148b

Finite packet densities

Outgoing scalar packet identification and normality › Finite packet densities · lines 890–906

Choose orthonormal $h_{1}, \dots, h_{m}$ in a common compact positive-frequency band. Set $b_{i} = b_{h_{i}}$ and

A_{ij} = ω_{U} (b_{j}^{†} b_{i}) = \int h_{i} h_{j} \frac{∣ τ ( ω ) ∣ ^{2}}{e ^{β ω} - 1} d ω .

This convention retains the covariance transposition: $ω_{U} (b_{i}^{†} b_{j}) = A_{j i}$ .

Let

D (z) = exp (i \sum z_{i} b_{i}^{†} - z_{i} b_{i}) .

Displayed formulas in this passage

unlabeled · line 894
$A_{ij} = ω_{U} (b_{j}^{†} b_{i}) = \int h_{i} h_{j} \frac{∣ τ ( ω ) ∣ ^{2}}{e ^{β ω} - 1} d ω .$
unlabeled · line 903
$D (z) = exp (i \sum z_{i} b_{i}^{†} - z_{i} b_{i}) .$