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Description
We study the lattice Hamiltonian formulation of quantum electrodynamics with staggered fermions and extend the mass-shift construction developed for the Schwinger model to the $(3+1)$-dimensional case. In the Schwinger model, the chiral transformation is realized as a one-site translation of the staggered fermion field. By introducing a correction term, referred to as the mass shift, the lattice Hamiltonian possesses an exact discrete chiral symmetry, while also allowing for the correct transformation of the $\theta$ parameter, leading to significantly improved convergence of numerical calculations.
In this work, we generalize this construction to $(3+1)$-dimensions and show that the resulting lattice Hamiltonian with the mass shift also possesses an exact discrete chiral symmetry. The realization of the $\theta$ parameter shift is left for future work.