A recursion relation for the Wick products of the CAR algebra

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In this paper we obtain an explicit recursion relation for the Wick products of the CAR algebra in terms of Wick products of lesser order and the bracket of the Fermi fields. This formula extends to Fermi fields the recursion formula given by I.E. Segal for Bose fields (cf. §1.4 in [I.E. Segal, Nonlinear functions of weak processes. I, J. Funct. Anal. 4 (1969) 404–456] and §7.1–7.2 in [J.C. Baez, I.E. Segal, Z. Zhou, Introduction to Algebraic and Constructive Quantum Field Theory, Princeton Univ. Press, NJ, 1992]).