  We investigate the properties of conduction electrons in single-walled
armchair carbon nanotubes (SWNT) in the presence of both transverse electric
and magnetic fields. We find that these fields provide a controlled means of
tuning low-energy band structure properties such as inducing gaps in the
spectrum, breaking various symmetries and altering the Fermi velocities. We
show that the fields can strongly affect electron-electron interaction,
yielding tunable Luttinger liquid physics, the possibility of spin-charge-band
separation, and a competition between spin-density-wave and charge-density-wave
order. For short tubes, the fields can alter boundary conditions and associated
single-particle level spacings as well as quantum dot behavior.
