A Global Theory of Parametrized Quantum Mechanics

  • Lay Nam Chang
  • Yigao Liang
Part of the NATO ASI Series book series (NSSB, volume 245)


We study the dependence of energy eigenvalues and eigenfunctions on parameters in the Hamiltonian from a global perspective. This dependence can be realized by topological quantum numbers in general. A general conservation law is found for these additive topological charges in the metamorphoses of energy bands. Many topological properties of “accidental” degeneracies are revealed with these results. In particular, global constraints can make degeneracies more generic (smaller codi-mension). Non-trivial topological charges can also tie energy bands together and make them inseparable. Generally, non-abelian structures arise due to metamorphoses of energy bands. These conclusions are very useful in understanding the meaning of higher cocycles in gauge theories.


Gauge Theory Vector Bundle Isomorphism Class Topological Charge Homotopy Group 
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  1. 1.
    L.N. Chang, Y. Liang, Mod. Phys. Lett. A3, 1839(1988)MathSciNetADSGoogle Scholar
  2. 2.
    L.N. Chang, Y. Liang, “A Topological Theory of Parametrized Quantum Mechanics”, preprint, April, 1989.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Lay Nam Chang
    • 1
  • Yigao Liang
    • 2
  1. 1.Department of PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of Physics and AstronomyUniversity of KentuckyLexingtonUSA

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