algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
field theory: classical, pre-quantum, quantum, perturbative quantum
In quantum field theory a quantum state is called quasi-free if
its n-point functions are non-vanishing only for even $n$;
its 2-point function determines all its $n$-point functions.
This reflects the structure of the Wick algebra of quantum observables for the free field.
Marek Radzikowski, p. 4 of Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys. 179 (1996), 529–553 (Euclid)
Igor Khavkine, Valter Moretti, section 2.4 of Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction, Chapter 5 in Romeo Brunetti et al. (eds.) Advances in Algebraic Quantum Field Theory, Springer, 2015 (arXiv:1412.5945)