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We describe the quantum interference of a single photon in the Mach-Zehnderinterferometer using the Heisenberg picture. Our purpose is to show that thedescription is local just like in the case of the classical electromagneticfield, the only difference being that the electric and the magnetic fields are,in the quantum case, operators (quantum observables). We then consider asingle-electron Mach-Zehnder interferometer and explain what the appropriateHeisenberg picture treatment is in this case. Interestingly, the paritysuperselection rule forces us to treat the electron differently to the photon.A model using only local quantum observables of different fermionic modes, suchas the current operator, is nevertheless still viable to describe phaseacquisition. We discuss how to extend this local analysis to coupled fermionicand bosonic fields within the same local formalism of quantum electrodynamicsas formulated in the Heisenberg picture.

Interference in the Heisenberg Picture of Quantum Field Theory, Local Elements of Reality and Fermions