ing from anomalous magnetic couplings. The resulting polarizabilities consequently have the correct physical interpretation, and correspond to those extracted from experiment, as well as those derived from chiral perturbation theory, for example. We consider both the neutron and proton in this study. For the latter, we use the relativistic generalization of the method proposed in [12], which relies on matching QCD correlators onto those derived from single-hadron effective actions. We have also employed this method recently for pseu- doscalar meson electric polarizabilities [13]. A salient feature of these computations is that they utilize a periodic lattice action with everywhere constant electric fields, and thereby eliminate difficulties arising from Dirichlet boundary conditions used in previous studies. 2 Our calculations of nucleon magnetic moments and electric polarizabilities include effects from dynamical quarks, however, they are restricted to electrically neutral sea quarks. We organize our presentation in the following manner. First in Sect. II, we analytically determine the form of baryon correlation functions in external electric fields. We specialize to the case of a uniform electric field, and derive results for both neutral and charged baryons. A key observation of this section is that baryon electric polarizabilities cannot be determined without knowledge of their magnetic moments. This is analogous to the experimental situation, where Born terms must be subtracted to extract polarizabilities from Compton scattering. Appendix A is concerned with the physics underlying the Born subtraction. In Sect. III, we provide the pertinent details of our lattice computations, and implementation of the background field. In Sect. IV, we present our analysis of nucleon correlation functions calculated in background electric fields using lattice QCD. For both the neutron and proton, we demonstrate that the measured correlation functions agree in form with the analytic expectations from the hadronic theory, and that magnetic moments and electric polarizabilities can be extracted from data. Appendix B is devoted to the analysis of unpolarized neutron correlators, from which consistent results are obtained. (These results, however, do not permit the determination of the electric polarizability—only a combination of the polarizability and the square of the magnetic moment. The latter contribution arises from Born-level couplings.) A brief conclusion in Sect. V ends our work. To extract properties of nucleons in background electric fields, we must first understand the expected behavior of their two-point correlation functions. In this section, we determine baryon two-point functions using the single-hadron effective action that arises from QCD in the ultra-low energy limit. The functional forms deduced for these two-point functions can then be utilized to fit baryon correlators computed with lattice QCD. From these fits, one can deduce hadronic parameters, such as the magnetic moments and electric polarizabilities. To arrive at a uniform electric field of the form ⃗ E = E ˆ z , we use the Euclidean space vector potential While there are other gauge equivalent choices, we find Eq. (1) particularly useful. 3 The A$_{µ}$ = (0 , 0 , −E x$_{4}$, 0) . (1) II. SPIN-HALF CORRELATION FUNCTIONS 2 Periodic actions with everywhere constant magnetic fields have also been employed recently to study magnetic moments of hadrons [14], and modification of the QCD vacuum [15, 16]. 3 On a torus, many of the gauge equivalent choices in infinite volume are no longer equivalent, but differ by their holonomy. External fields with non-vanishing holonomy lead to new interactions that are finite 3