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References
Commutativity of fields at spacelike separations is an important physical requirement. It can be considered an axiom of field theory in the Wightman formulation, see R.F. Streater and A.S. Wightman, PCT, Spin and Statistics and All That, W.A. Benjamin, Inc. (1964). The relation between causal propagation of fields and antiparticles is also discussed in R.P. Feynman, “The Reason for Antiparticles” in Elementary Particles. and the Laws of Physics, Oxford University Press (1987).
The importance of the Feynman propagator was realized by Stückelberg, Feynman and Dyson, see J. Schwinger, Selected Papers in Quantum Electrodynamics, Dover Publications, Inc. (1958); S. S. Schweber, QED and the Men Who Made It, Princeton University Press (1994).
For Grassmann variables applied to field theory, the original reference is F.A. Berezin, The Method of Second Quantization, Academic Press (1966). Grassmann variables have been used in Statistical Mechanics for evaluation of partition functions, some scattering problems, etc. For an interesting solution of the Ising model using Grassmann variables, see S. Samuel, J. Math. Phys. 19, 1438 (1978).
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(2005). Commutators and Propagators. In: Quantum Field Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-25098-0_4
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