A topological investigation of the quantum adiabatic phase
type: Item
instance of: scholarly article
title: A topological investigation of the quantum adiabatic phase
zbMATH Open document ID: 0625.55014
DOI: 10.1007/BF01238907
author: Elias Kiritsis
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 55S40
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 4015711
zbMATH Keywords: first Chern class
zbMATH Keywords: principal bundles over spheres
zbMATH Keywords: nth-level Hilbert subbundle
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: obstructions to a continuous definition of the phase of a transported wave-function
zbMATH Keywords: adiabatic transport
zbMATH Keywords: universal U(n)-bundles
zbMATH Keywords: sections of U(n)-bundles over \({bbfC}P(n)\)
zbMATH Keywords: homotopy lifting property
zbMATH Keywords: transport of an n-fold degenerate level
zbMATH Keywords: quantum adiabatic phase
zbMATH Keywords: gauge bundles
zbMATH Keywords: Hamiltonian in the space of wave-functions
zbMATH Keywords: field theory anomalies
zbMATH Keywords: Nielsen-Ninomiya theorem
MaRDI profile type: Publication
cites work: Hamiltonian interpretation of anomalies
cites work: Q5825483
cites work: Q4192669
description: scientific article; zbMATH DE number 4015711