Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations

Journal of Mathematical Physics

Volumn 40, Issue 1, 1999, Pages 49-63

  Doebner, H D ^a   Goldin, G A ^b   Nattermann, P ^a  

^a CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475658     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532786     Document Type: Article

References (30)

1. H.-D. Doebner and G. A. Goldin, Phys. Rev. A 54, 3764 (1996).
2. M. D. Kostin, J. Chem. Phys. 57, 3589 (1972).
3. I. Bialynicki-Birula and J. Mycielski, Ann. Phys. (N.Y.) 100, 62 (1976).
4. F. Guerra and M. Pusterla, Lett. Nuovo Cimento 34, 351 (1982).
5. H.-D. Doebner and G. A. Goldin, Phys. Lett. A 162, 397 (1992).
6. H.-D. Doebner and G. A. Goldin, J. Phys. A 27, 1771 (1994)
7. P. Nattermann, in Proceedings of the XXVI Symposium on Mathematical Physics, Torun, Poland, 7-10 December, 1993 (Nicolas Copernicus University Press, Torun, 1994), p. 47.
8. P. Nattermann, Rep. Math. Phys. 36(2/3), 387 (1995).
9. H.-D. Doebner, G. A. Goldin, and P. Nattermann, in Quantization, Coherent States, and Complex Structures, edited by J.-P. Antoine, S. T. Ali, W. Lisiecki, I. M. Mladenov, and A. Odzijewicz (Plenum, New York, 1995), p. 27.
10. G. A. Goldin, in Nonlinear, Deformed, and Irreversible Quantum Systems, edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann (World Scientific, Singapore, 1995), p. 125.
11. P. Nattermann and W. Scherer, in Ref. 10, p. 188.
12. R. P. Feynman and A. R. Hibbs. Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965), p. 96.
13. E. Nelson, Phys. Rev. 150, 1079 (1966).
14. This perspective is consistent with the discussion given by B. Mielnik, Commun. Math. Phys. 37, 221 (1974).
15. W. Lücke, in Ref. 10, p. 140.
16. P. Nattermann, Generalized Quantum Mechanics and Nonlinear Gauge Transformations, in Symmetry in Science, Vol. IX, edited by B. Gruber and M. Ramek (Plenum, New York, 1997), p. 269; quant-ph/9703017.
17. G. A. Goldin and G. Svetlichny, J. Math. Phys. 35, 3322 (1994).
18. W. Lücke and P. Nattermann, Nonlinear Quantum Mechanics and Locality, in Symmetry in Science Vol. X, edited by B. Gruber and M. Ramek (New York, Plenum, 1998), p. 197; quant-ph/9707055.
19. G. Rideau and P. Wintern tz, J. Math. Phys. 34, 558 (1993).
20. H.-D. Doebner and G. A. Goldin, in Particles and Fields, edited by H.-D. Doebner, R. Raczka, and M. Pawlowski (World Scientific, Singapore, 1993), p. 115.
21. R. Dashen and D. H. Sharp, Phys. Rev. 165, 1867 (1968).
22. G. A. Goldin and D. H. Sharp, in Group Representations in Mathematics and Physics, edited by V. Bargmann, Lecture Notes in Physics Vol. 6 (Springer, Berlin, 1970), p. 300.
23. G. A. Goldin, J. Math. Phys. 12, 462 (1971).
24. B. Angermann, H.-D. Doebner, and J. Tolar, in Nonlinear Partial Differential Operators and Quantization Procedures, edited by S. I. Andersson and H.-D. Doebner, Lecture Notes in Mathematics Vol. 1037 (Springer, Berlin, 1983), p. 171.
25. H.-D. Doebner and J. D. Hennig, A Quantum Mechanical Evolution Equation for Mixed States from Symmetry and Kinematics, in Symmetries in Science Vol. VIII, edited by B. Gruber (Plenum, New York, 1995), p. 85.
26. H.-D. Doebner and P. Nattermann, Acta Phys. Pol. B 27, 2327 (1996); 27, 4003 (1996).
27. H.-D. Doebner and P. Nattermann, Acta Phys. Pol. B 27, 2327 (1996); 27, 4003 (1996).
28. N. Gisin, Phys. Lett. A 143, 1 (1990).
29. J. Polchinski. Phys. Rev. Lett. 66, 397 (1991).
30. N. Gisin, in Ref. 10, p. 109.