Anticipations of the Geometric Phase

DEC 01, 1990

The notion that a quantum system’s wovefunction may not return to its original phase after its parameters cycle slowly around a circuit had many precursors—in polarized light, radio waves, molecules, matrices and curved surfaces.

DOI: 10.1063/1.881219

Michael Berry

In science we like to emphasize the novelty and originality of our ideas. This is harmless enough, provided it does not blind us to the fact that concepts rarely arise out of nowhere. There is always a historical context, in which isolated precursors of the idea have already appeared. What we call “discovery” sometimes looks, in retrospect, more like emergence into the air from subterranean intellectual currents.

References

1. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984);
reprinted in ref. 2, p.124.
2. A. Shapere, F. Wilczek, eds., Geometric Phases in Physics, World Scientific, Singapore (1989).
3. R. Jackiw, Commun. At. Mol. Phys. 21, 71 (1988).
J. W. Zwanziger, M. Koenig, A. Pines, Annu. Rev. Phys. Chem. (1990), in press.
4. B. Markovski, V. I. Vinitsky, Topological Phases in Quantum Theory, World Scientific, Singapore (1989).
5. M. V. Berry, in Anomalies, Phases, Defects, M. Bregola, G. Marmo, G. Morandi, eds., Bibliopolis, Naples (1990), p. 125.
6. S. M. Rytov, Dokl. Akad. Nauk. USSR 18, 263 (1938);
reprinted in ref. 4, p. 6.
V. V. Vladimirskii, Dokl. Akad. Nauk. USSR 21, 222 (1941);
reprinted in ref. 4, p. 11.
7. M. V. Berry, Nature 326, 277 (1987); https://doi.org/NATUAS
reprinted in ref. 2, p. 197.
8. M. V. Berry, in Fundamental Aspects of Quantum Theory, NATO Adv. Stud. Inst. Ser., vol. 144, V. Gorini, A. Frigerio, eds., Plenum, New York (1986), p. 267.
9. S. Pancharatnam, Proc. Ind. Acad. Sci. A 44, 247 (1956);
reprinted in ref. 2, p. 51.S. Ramaseshan, R. Nityananda, Curr. Sci. (India) 55, 1225 (1986).
10. M. V. Berry, J. Mod. Opt. 34, 1401 (1987); https://doi.org/JMOPEW
reprinted in ref. 2, p. 67.
11. M. S. Smith, Proc. R. Soc. London, Ser. A 346, 59 (1975).
K. G. Budden, M. S. Smith, Proc. R. Soc. London, Ser. A 350, 27 (1975).
12. M. V. Berry, Proc. R. Soc. London (1990), in press.
13. H. C. Longuet‐Higgins, U. Öpik, M. H. L. Pryce, R. A. Sack, Proc. R. Soc. London, Ser. A 244, 1 (1958).
14. G. Herzberg, H. C. Longuet‐Higgins, Faraday Soc. Disc. 35, 77 (1963);
reprinted in ref. 2, p. 74.
15. G. Delacrétaz, E. R. Grant, R. L. Whetten, L. Wöste, J. W. Zwanziger, Phys. Rev. Lett. 56, 2598 (1986); https://doi.org/PRLTAO
reprinted in ref. 2, p. 240.
16. V. I. Arnold, Mathematical Methods of Classical Dynamics, Springer‐Verlag, New York (1978).
17. K. Uhlenbeck, Am. J. Math. 98, 1059 (1976).https://doi.org/AJMAAN
18. G. Darboux, Lecons sur la Théorie Générale des Surfaces, vol. 4, Gauthier‐Villars, Paris (1896), note VII, p. 448.
19. M. V. Berry, J. H. Hannay, J. Phys. A 10, 1809 (1977).https://doi.org/JPHAC5
20. F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).
21. M. V. Berry, in Sir Charles Frank 80th Birthday Festschrift, R. G. Chambers, J. E. Enderby, A. Keller, A. R. Lang, J. W. Steeds, eds., Adam Hilger, Bristol (1990), in press.
22. A. J. Stone, Proc. R. Soc. London, Ser. A 351, 141 (1976);
reprinted in ref. 2, p. 80.
23. C. A. Mead, D. G. Truhlar, J. Chem. Phys. 70, 2284 (1979); https://doi.org/JCPSA6
reprinted in ref. 2, p. 90.
24. M. V. Berry in reference 2, p. 26.

More about the Authors

Michael Berry. University of Bristol, Bristol, England.