  Understanding the transitions of nucleons into various resonance structures
through electromagnetic interactions plays a pivotal role in advancing our
comprehension of the strong interactions within the domain of quark
confinement. Furthermore, gaining precise insights into the elastic and
resonance structures of nucleons is indispensable for deciphering the physics
from neutrino-nucleus scattering cross sections experimental data, which remain
theoretically challenging, even in the context of neutrino-nucleon interactions
whose profound understanding is imperative for the neutrino oscillation
experiments. One promising avenue involves the direct evaluation of the
lepton-nucleon scattering cross sections across quasi-elastic, resonance,
shallow-inelastic, and deep inelastic regions, which can be achieved through
the hadronic tensor formalism in lattice QCD. In this work, we present the
determination of the nucleon's Sachs electric form factor using the hadronic
tensor formalism and verify that it is consistent with that from the
conventional three-point function calculation. We additionally obtain the
transition form factor from the nucleon to its first radial excited state
within a finite volume. Consequently, we identify the latter with the
nucleon-to-Roper transition form factor $G_E^*(Q^2)$, determine the
corresponding longitudinal helicity amplitude $S_{1/2}(Q^2)$ and compare our
findings with experimental measurements, for the first time using the hadronic
tensor formalism. The limitations and systematic improvements of the approach
are also discussed.
