  We investigate the effects of rotation on the excited bands of a tight
binding lattice, focusing particulary on the first excited (p-) band. Both the
on-site energies and the hopping between lattice sites are modified by the
effective magnetic field created by rotation, causing a non-trivial splitting
and magnetic fine structure of the p-band. We show that Peierls substitution
can be modified to describe p-band under rotation, and use this method to
derive an effective Hamiltonian. We compare the spectrum of the effective
Hamiltonian with a first principles calculation of the magnetic band structure
and find excellent agreement, confirming the validity of our approach. We also
discuss the on-site interaction terms for bosons and argue that many-particle
phenomena in a rotating p-band can be investigated starting from this effective
Hamiltonian.
