We introduce a notion of strongly C×-graded, or equivalently, C/Zgraded generalized g-twisted V -module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V -module if V admits an additional C-grading compatible with g. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0)...

For a spin subjected to an adiabatically changing magnetic field, the " solid angle result " as embodied by a rotation operator is the only non-trivial factor in the evolution operator. For a charged particle, the infinite degeneracy of the energy levels calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator ...

For a spin subjected to an adiabatically changing magnetic field, the ”solid angle result” as embodied by a rotation operator is the only nontrivial factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator that enters into...