Let $H$ be a real Hilbert space with
complexification $H\_{\mathbb{C}}$. We denote by $\mathfrak{F}$ the antisymmetric Fock space
over $H\_\mathbb{C}$ ("fermions"). A creation operator is denoted by $c(f)$.
I need a reference for the calculus of
$$
\langle\,\Omega ,\big(c(f\_1)+c(f\_1)^\*\big)...\big(c(f\_{2k})+c(f\_{2k})^\*\big)\Omega\,\rangle\_{\mathfrak{F}}
$$
where $\Omega$ the unit vector, called vacuum.


Thank you.



Reference for Wick product
The answer is provided by the article


* Edward G. Effros and Mihai Popa, *Feynman diagrams and Wick products associated with q-Fock space*, PNAS 100 (15) (2003) 8629-8633, <https://doi.org/10.1073/pnas.1531460100>


However, the authors work in the context of $q$-Fock space. I does not know if there exists an older paper which provides the answer in the less general context of antisymmetric Fock space (i.e. q=1).


