Manuscript V@1 · V.tex · section · e7ddf37d

Mixed Wick product and retarded coefficient

The one-oscillator mixed insertion › Mixed Wick product and retarded coefficient · lines 2651–2671

For clarity about the particle blocks, define

w_{+} = \frac{v _{e} + i v _{r}}{2}, w_{-} = \frac{v _{e} - i v _{r}}{2} .

Antilinearity of annihilation gives

R_{g, f} = b a (w_{+}) + b a^{†} (w_{-}) + b^{†} a (w_{-}) + b^{†} a^{†} (w_{+}) .

These are mixed pair annihilation, two exchange terms, and mixed pair creation. They are finite-rank cross kernels, not estimates for a dense gravitational one-particle space.

Figure fig:mixed-blocks-locality displays the mixed particle blocks and the finite-mode locality limitation.

Displayed formulas in this passage

unlabeled · line 2654
$w_{+} = \frac{v _{e} + i v _{r}}{2}, w_{-} = \frac{v _{e} - i v _{r}}{2} .$
unlabeled · line 2659
$R_{g, f} = b a (w_{+}) + b a^{†} (w_{-}) + b^{†} a (w_{-}) + b^{†} a^{†} (w_{+}) .$

Mixed Wick product and retarded coefficient

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