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Wick product of free fields and wave front sets in the sense of Lars Hörmander

The answer to both questions is no. This is due to two facts: The Klein-Gordon two-point distribution $\omega_2(x,y)=\langle\Omega,\phi(x)\phi(y)\Omega\rangle$ in $\mathbb{R}^4$, where $\Omega_1=\...
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