Quantum Adiabatic Phases And Chiral Gauge Anomalies

  • Gordon W. Semenoff†
Part of the NATO Science Series book series (NSSB, volume 160)


The quantum adiabatic phase [1,2] has recently emerged as a universal element in the topological analysis of various quantum mechanical problems. It can be understood as an Ahoronov-Bohm effect on the parameter space of a quantum mechanical system and has seen numerous applications, notably to the analysis of corrections to semiclassical quantization [2,3,4], the statistics of quasiparticles such as vortices in two dimensional systems [6,6,7], adiabatic effective actions, the quantum Hall effect [8] and chiral anomalies in the Hamiltonian, Schrödinger picture of gauge theories [9]. Furthermore, some of its predicted interference phenomena have recently found good agreement with experiment [10,11]. In this review we shall give a simple account of the origin of the quantum adiabatic phase, describe how the concept is used to construct adiabatic effective actions and discuss chiral gauge anomalies within this framework.


Gauge Theory Gauge Symmetry Gauge Field Quantum Hall Effect Chiral Anomaly 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.V. Berry , Proc. Roy. Soc. Lond. Ser392, 45 (1984); B. Simon, Phys. Rev. Lett. 51, 2167 (1983); L. Schiff, “Quantum Mechanics” (McGraw-Hill, New York 1955) pg. 290. Google Scholar
  2. 2.
    F. Wilczek, A. Zee, Phys. Rev. Lett. 52, 2111 (1984). J. Moody, A. Shapere, F. Wilczek, Phys. Rev. Lett. 56, 893 (1986); R. Jackiw, Phys. Rev. Lett. 56 2779 (1986). MathSciNetADSCrossRefGoogle Scholar
  3. M. Kuratsuji, S. Iida, Phys. Lett. 111A, 220 (1985).ADSGoogle Scholar
  4. A. Niemi, G. Semenoff, Phys. Rev. Lett. 55, 227 (1985).ADSGoogle Scholar
  5. D. Arovas, R. Schrieffer, F. Wilczek, Phys. Rev. Lett. 53, 772 (1984).ADSCrossRefGoogle Scholar
  6. 6.
    D. Arovas, R. Schrieffer, F. Wilczek, A. Zee, Nucl. Phys. B25l[FS13], 117 (1985). MathSciNetCrossRefGoogle Scholar
  7. D. Haldane, Yong-Shi Wu, Phys. Rev. Lett. 55, 2287 (1985).ADSGoogle Scholar
  8. G. Semenoff, P. Sodano, Phys. Rev. Lett. 57, 1195 (1986).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    P. Nelson, L. Alvarez-Gaume, Comm. Math. Phys. 99, 103 (1985); A. Niemi, G. Semenoff, réf. 2 and Phys. Rev. Lett. 56, 1019 (1986); H. Sonoda, Phys. Lett. 156B, 220 (1985); Nucl. Phys. B266, 440 (1986); A. Niemi, G. Semenoff and Yong-Shi Wu, Nucl. Phys. B276, 173 (1986). MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    M. V. Berry, Bristol Preprint, 1986 R. Chiao, Yong-Shi Wu, Phys. Rev. Lett. 57, 933 (1986). ADSCrossRefGoogle Scholar
  11. 11.
    A. Tomita, R. Chiao, Phys. Rev. Lett. 57, 937 (1986); R. Chiao, private communication. ADSCrossRefGoogle Scholar
  12. J. Von Neumann, E. Wigner, Z. Phys. 30, 467 (1929).Google Scholar
  13. T.T. Wu, C.N. Yang, Nucl. Pyhs. B107, 365 (1976).MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    L. Faddeev, Phys. Lett. B145, 81 (1984); L. Faddeev, S. Shatashvili, Teor. Math. Fiz. 60, 206 (1984); J. Mickelsson, Comm. Math. Phys. 97, 361 (1984); I. Frenkel and I. Singer, unpublished. MathSciNetADSGoogle Scholar
  15. A. Niemi, G. Semenoff, Phys. Lett, in press (1986).Google Scholar
  16. 16.
    See B. Grossman, Rockefeller University Report, 1986.Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Gordon W. Semenoff†
    • 1
  1. 1.Department of PhysicsUniversity of British Columbia VancouverBritish ColumbiaCanada

Personalised recommendations