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.
%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
}