  We compute the electronic band structure and optical properties of boron
arsenide using the relativistic quasiparticle self-consistent $GW$ approach,
including electron-hole interactions through solution of the Bethe-Salpeter
equation. We also calculate its electronic and optical properties using
standard and hybrid density functional theory. We demonstrate that the
inclusion of self-consistency and vertex corrections provides substantial
improvement in the calculated band features, in particular when comparing our
results to previous calculations using the single-shot $GW$ approach and
various DFT methods, from which a considerable scatter in the calculated
indirect and direct band gaps has been observed. We find that BAs has an
indirect gap of 1.674 eV and a direct gap of 3.990 eV, consistent with
experiment and other comparable computational studies. Hybrid DFT reproduces
the indirect gap well, but provides less accurate values for other band
features, including spin-orbit splittings. Our computed Born effective charges
and dielectric constants confirm the unusually covalent bonding characteristics
of this III-V system.
