where the electromagnetically gauge covariant derivative is D$_{µ}$ = ∂$_{µ}$ + iQA$_{µ}$ , and higher- order terms in the field strength appear parametrically in the E -dependent couplings in Eq. (10). The parameter E ( E ) is the charged particle’s rest energy, which has the weak field expansion in Eq. (3). The anomalous magnetic moment coupling, ˜ µ ( E ), has a weak field expansion in even powers of the field, and satisfies the zero-field relation, ˜ µ (0) = ˜ µ . The action in Eq. (10) describes the proton in the ultra-low energy regime of QCD. As with the neutral baryons, it is beneficial to consider boost-projected correlation functions. For charged baryons, these have the form G$_{±}$ ( x$_{4}$, E ) = Z ( E ) ( 1 ± ˜ µ E 2 M 2 ) D ( x$_{4}$, E$_{eff}$ ( E ) 2 ∓ Q E , E ) , (11) D ( x$_{4}$, E $^{2}$, E ) = ∫ ∞ 0 ds √ Q E 2 π sinh( Q E s ) exp [ − 1 2 Q E x 2 $_{4}$coth( Q E s ) − 1 2 E $^{2}$s ] . (12) where the function D ( x$_{4}$, E $^{2}$, E ) is the relativistic propagator function [20] When the charge is set to zero, we recover the neutral baryon correlation functions in Eq. (9). As one can see, to determine charged baryon electric polarizabilities, we must also deduce their anomalous magnetic moments. This can be achieved utilizing both boost-projected correlation functions. These fits are more complicated than for neutral hadrons; however, the function in Eq. (12) also describes the propagation of a charged scalar in an electric field, and our previous study demonstrated that such fits can be carried out [13]. III. LATTICE DETAILS To demonstrate our method for extracting nucleon magnetic moments and electric polarizabilities from lattice two-point functions, we have employed an ensemble of anisotropic gauge configurations with (2+1)-flavors of dynamical clover fermions [22, 23]. Our ensemble consists of 200 lattices of size L 3 × β = 20 3 × 128. After an initial 1000 thermalization trajectories, the lattices were chosen from an ensemble of 7000 spaced either by 20 or 40 trajectories to minimize autocorrelations. The lattice spacing in the spatial directions is a$_{s}$ = 0 . 123(3) fm [22, 23], with a non-perturbatively tuned anisotropy parameter of ξ ≡ a$_{s}$/a$_{t}$ = 3 . 5, where a$_{t}$ is the temporal lattice spacing. The finer temporal spacing is a crucial feature for this study, as it allows us to fit reliably more complicated functional forms for the time-dependence of correlation functions. For this ensemble, the renormalized strange quark mass is near the physical value, while the renormalized light quark mass leads to a pion mass of m$_{π}$ ≈ 390 MeV . On each configuration, we compute at least 10 propagators for each of the up, down, and strange quarks with random spatial source locations. Multiple inversions were made efficient using the EigCG inverter implemented in the Chroma lattice field theory library [24]. Interpolating fields at the source are generated from gauge-covariantly Gaussian-smeared quark fields [25, 26] on a stout-smeared [27] gauge field in order to optimize the overlap onto the ground state in the absence of background fields. Interpolating fields at the sink are constructed from local quark fields. Each propagator is located with source time at ( x$_{4}$ )$_{src}$ = 0. Randomization of the source time location, while improving the statistical sampling, would complicate the determination of charged baryon correlation functions, as 6