A novel nonlocal spin-1/2 theory: classical and quantum aspects

We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale $\Lambda$. We minimally couple a $U(1)$ gauge field to the nonlocal spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the $g$-factor of massive particles.