  The parity-expanded variational analysis (PEVA) technique enables the
isolation of opposite-parity eigenstates at finite momentum. The approach has
been used to perform the first lattice QCD calculations of excited-baryon form
factors. In particular, these calculations show that the low-lying odd-parity
nucleon excitations are described well by constituent quark models at moderate
u and d quark masses approaching the strange quark mass. Herein, we extend the
PEVA technique to establish a formalism for the determination of odd-parity
nucleon electromagnetic transition form factors in lattice QCD. The formalism
is implemented in the first calculation of the helicity amplitudes for
transitions from the ground state nucleon to the first two odd-parity
excitations. Through a comparison with constituent quark model calculations of
these amplitudes, these new results give important insight into the structure
of these excitations. This work is a critical step towards confronting
experimental electroproduction amplitudes for the $N^*(1535)$ and $N^*(1650)$
resonances with ab-initio lattice QCD calculations.
