A topological investigation of the quantum adiabatic phase
Using algebraic topology the appearance of the quantum adiabatic phase over various parameter manifolds is investigated. The relation with nontrivial gauge bundles (both abelian and nonabelian) is studied and it is shown that the phase appears as a result of homotopically nontrivial mappings, induced by the Hamiltonian in the space of wave-functions. The cohomological picture is developed and some topological considerations concerning field theory anomalies in the Hamiltonian picture are presented. A proof of the Nielsen-Ninomiya theorem is given inspired from the notion of the adiabatic phase.
obstructions to a continuous definition of the phase of a transported wave-function
sections of U(n)-bundles over \({bbfC}P(n)\)
Hamiltonian in the space of wave-functions
scientific article; zbMATH DE number 4015711