%0 Journal Article %1 kiritsis1987topological %A Kiritsis, Elias %D 1987 %I Springer-Verlag %J Communications in Mathematical Physics %K adiabatic quantum topology %N 3 %P 417-437 %R 10.1007/BF01238907 %T A topological investigation of the Quantum Adiabatic Phase %U http://dx.doi.org/10.1007/BF01238907 %V 111 %X 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 non-abelian) is studied and it is shown that the phase appears as a result of homotopically non-trivial 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.

@article{kiritsis1987topological, abstract = {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 non-abelian) is studied and it is shown that the phase appears as a result of homotopically non-trivial 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.}, added-at = {2013-02-06T00:40:30.000+0100}, author = {Kiritsis, Elias}, biburl = {https://www.bibsonomy.org/bibtex/2a369439bf1a241d2767c79a3f4f68b09/ttuegel}, doi = {10.1007/BF01238907}, interhash = {ad194eae970cf47d7a88079027983f1e}, intrahash = {a369439bf1a241d2767c79a3f4f68b09}, issn = {0010-3616}, journal = {Communications in Mathematical Physics}, keywords = {adiabatic quantum topology}, language = {English}, number = 3, pages = {417-437}, publisher = {Springer-Verlag}, timestamp = {2013-02-06T00:40:30.000+0100}, title = {A topological investigation of the Quantum Adiabatic Phase}, url = {http://dx.doi.org/10.1007/BF01238907}, volume = 111, year = 1987 }