FSD expansion () we are ready to compute the electromagnetic form factors directly from the regularized action () which includes the fermion loop corrections. The nucleon electromagnetic Sachs form factors are defined by:

$$\openup 2\jot
\eqalignno{
\langle N(p)\vert j_0^{em}(0)\vert N(p')\rangle &= G_E(q^2)
\ , &(\FFDEFa) \cr
\langle N(p)\vert j_i^{em}(0)\vert N(p')\rangle &=
{1\over 2{\cal M}_N} \ G_M(q^2) \ i \
\epsilon_{ikl} \, q^k \langle N \vert \sigma^l \vert N \rangle
\ , &(\FFDEFb) }$$

where $\vert N(p') \rangle$ is the nucleon state with proper spin and isospin quantum numbers. The electromagnetic current $j^{em}_{\mu}(x)$ is in the Minkowski space-time and ${\cal M}_N$ is the nucleon mass. It is clear from () that to compute the electromagnetic form factors we need the current evaluated in the previous Section. The isoscalar and isovector parts of the form factors are defined by:

$$G_{E,M} \equiv {1\over 2}\ G_{E,M}^{T=0} + \hat T_3 \
G^{T=1}_{E,M}
\ . \eqno(\FFSV)$$

The Sachs form factors () are appropriate for the non-relativistic limit (${\vec q\,}^2 \ll {\cal M}_N$) that is consistent with the large $N_c$ approximation.

The isoscalar form factors (electric and magnetic) come from the scalar part of the quark current matrix $\hat Q$ ($\sim \hat 1$) while the isovector form 