A theory of quantum electrodynamics with nonlocal interaction

In this paper, we present a theory of quantum electrodynamics with nonlocal interaction, a main characteristic of the theory is that a charged particle situated x^{mu} interacts with electromagnetic field situated y^{mu}, where x^{mu}=y^{mu}+aA^{mu}, A^{mu} reads electromagnetic 4-potential, a is a constant. All the action, the equations of motion of charged particle and electromagnetic field are given. For the case of free fields, charged particle and electromagnetic field obey the Dirac equation and the Maxwell equation of free fields, respectively; for the case with interaction, both the equations of motion of charged particle and electromagnetic field lead to current conservation j^{mu}_{,mu}=0 naturally. The theory is Lorentz invariant and gauge invariant under a generalized gauge transformation, the generalized gauge transformation can guarantee that the temporal gauge condition A^{0} holds or the Lorentz gauge condition A^{mu}_{,mu}=0 holds, respectively. The theory returns to the current QED when a=0. Finally, taking advantage of the Lehmann-Symanzik-Zimmermann approach, we establish the corresponding quantum theory.