Quantization ambiguity, ergodicity and semiclassics

New Journal of Physics

Volumn 4, Issue , 2002, Pages

  Kaplan, Lev ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042513988     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/4/1/390     Document Type: Article

References (56)

1. Dirac P A M 1967 Lectures on Quantum Mechanics (New York: Academic)
2. Wilkinson M 1988 J. Phys. A: Math. Gen. 21 1173
3. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
4. Ali M K 1996 Can. J. Phys. 74 255
5. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
6. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
7. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
8. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
9. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
10. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
11. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
12. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
13. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
14. A few key papers on the vast subject of constrained quantization include Cheng K S 1972 J. Math. Phys. 13 1723 DeWitt B S 1957 Rev. Mod. Phys. 29 377 Jensen H and Koppe H 1971 Ann. Phys., NY 63 586 Batalin I A, Fradkin E S and Fradkina T E 1990 Nucl. Phys. B 332 723 Batalin I A and Fradkin E S 1989 Nucl. Phys. B 326 701 Faddeev L D 1970 Theor. Math. Phys. 1 1 Sniatycki J 1980 Geometric Quantization and Quantum Mechanics (New York: Springer) Kimura T 1971 Prog. Theor. Phys. 46 1261 da Costa R C T 1981 Phys. Rev. A 23 1982 De Oliveira N T and Lobo R 1982 Nuovo Cimento B 71 196
15. Schulman L S 1981 Techniques and Applications of Path Integration (New York: Wiley)
16. Arnol'd V I 1978 Mathematical Methods of Classical Mechanics (New York: Springer) Lanczos C 1986 The Variational Principles of Mechanics (New York: Dover)
17. Arnol'd V I 1978 Mathematical Methods of Classical Mechanics (New York: Springer) Lanczos C 1986 The Variational Principles of Mechanics (New York: Dover)
18. Mitchell K A 2001 Phys. Rev. A 63 042112 Maraner P 1995 J. Phys. A: Math. Gen. 28 2939 Maraner P and Destri C 1993 Mod. Phys. Lett. A 8 861 Kaplan L, Maitra N T and Heller E J 1997 Phys. Rev. A 56 2592
19. Mitchell K A 2001 Phys. Rev. A 63 042112 Maraner P 1995 J. Phys. A: Math. Gen. 28 2939 Maraner P and Destri C 1993 Mod. Phys. Lett. A 8 861 Kaplan L, Maitra N T and Heller E J 1997 Phys. Rev. A 56 2592
20. Mitchell K A 2001 Phys. Rev. A 63 042112 Maraner P 1995 J. Phys. A: Math. Gen. 28 2939 Maraner P and Destri C 1993 Mod. Phys. Lett. A 8 861 Kaplan L, Maitra N T and Heller E J 1997 Phys. Rev. A 56 2592
21. Mitchell K A 2001 Phys. Rev. A 63 042112 Maraner P 1995 J. Phys. A: Math. Gen. 28 2939 Maraner P and Destri C 1993 Mod. Phys. Lett. A 8 861 Kaplan L, Maitra N T and Heller E J 1997 Phys. Rev. A 56 2592
22. Kaplan L 1998 Phys. Rev. E 58 2983 Kaplan L 1998 Phys. Rev. Lett. 81 3371
23. Kaplan L 1998 Phys. Rev. E 58 2983 Kaplan L 1998 Phys. Rev. Lett. 81 3371
24. Vergini E G 2000 J. Phys. A: Math. Gen. 33 4709 Vergini E G and Carlo G G 2000 J. Phys. A: Math. Gen. 33 4717
25. Vergini E G 2000 J. Phys. A: Math. Gen. 33 4709 Vergini E G and Carlo G G 2000 J. Phys. A: Math. Gen. 33 4717
26. Main J 1999 Phys. Rep. 316 233 Weibert K, Main J and Wunner G 2001 Phys. Lett. A 289 329
27. Main J 1999 Phys. Rep. 316 233 Weibert K, Main J and Wunner G 2001 Phys. Lett. A 289 329
28. Prosen T and Robnik M 1993 J. Phys. A: Math. Gen. 26 L37
29. Rahav S, Agam O and Fishman S 1999 J. Phys. A: Math. Gen. 32 7093
30. Primack H and Smilansky U 2000 Phys. Rep. 327 1 Primack H and Smilansky U 1998 J. Phys. A: Math. Gen. 31 6253 see also Prosen T 1997 Phys. Lett. A 233 323
31. Primack H and Smilansky U 2000 Phys. Rep. 327 1 Primack H and Smilansky U 1998 J. Phys. A: Math. Gen. 31 6253 see also Prosen T 1997 Phys. Lett. A 233 323
32. Primack H and Smilansky U 2000 Phys. Rep. 327 1 Primack H and Smilansky U 1998 J. Phys. A: Math. Gen. 31 6253 see also Prosen T 1997 Phys. Lett. A 233 323
33. Boasman P A 1994 Nonlinearity 7 485
34. Shnirelman A I 1974 Usp. Mat. Nauk 29 181 Colin de Verdiere Y 1985 Commun. Math. Phys. 102 497 Zelditch S 1987 Duke Math. J. 55 919 Zelditch S and Zworski M 1996 Commun. Math. Phys. 175 673
35. Shnirelman A I 1974 Usp. Mat. Nauk 29 181 Colin de Verdiere Y 1985 Commun. Math. Phys. 102 497 Zelditch S 1987 Duke Math. J. 55 919 Zelditch S and Zworski M 1996 Commun. Math. Phys. 175 673
36. Shnirelman A I 1974 Usp. Mat. Nauk 29 181 Colin de Verdiere Y 1985 Commun. Math. Phys. 102 497 Zelditch S 1987 Duke Math. J. 55 919 Zelditch S and Zworski M 1996 Commun. Math. Phys. 175 673
37. Shnirelman A I 1974 Usp. Mat. Nauk 29 181 Colin de Verdiere Y 1985 Commun. Math. Phys. 102 497 Zelditch S 1987 Duke Math. J. 55 919 Zelditch S and Zworski M 1996 Commun. Math. Phys. 175 673
38. O'Connor P W and Heller E J 1989 Phys. Rev. Lett. 61 2288 Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 J. Phys. A: Math. Gen. 26 6217 Tanner G 1997 J. Phys. A: Math. Gen. 30 2863 Espinoza Ortiz J S and Ozorio de Almeida A M 1997 J. Phys. A: Math. Gen. 30 7301
39. O'Connor P W and Heller E J 1989 Phys. Rev. Lett. 61 2288 Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 J. Phys. A: Math. Gen. 26 6217 Tanner G 1997 J. Phys. A: Math. Gen. 30 2863 Espinoza Ortiz J S and Ozorio de Almeida A M 1997 J. Phys. A: Math. Gen. 30 7301
40. O'Connor P W and Heller E J 1989 Phys. Rev. Lett. 61 2288 Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 J. Phys. A: Math. Gen. 26 6217 Tanner G 1997 J. Phys. A: Math. Gen. 30 2863 Espinoza Ortiz J S and Ozorio de Almeida A M 1997 J. Phys. A: Math. Gen. 30 7301
41. O'Connor P W and Heller E J 1989 Phys. Rev. Lett. 61 2288 Sieber M, Smilansky U, Creagh S C and Littlejohn R G 1993 J. Phys. A: Math. Gen. 26 6217 Tanner G 1997 J. Phys. A: Math. Gen. 30 2863 Espinoza Ortiz J S and Ozorio de Almeida A M 1997 J. Phys. A: Math. Gen. 30 7301
42. Bäcker A, Schubert R and Stifter P 1997 J. Phys. A: Math. Gen. 30 6783
43. Berry M V 1977 J. Phys. A: Math. Gen. 10 2083 Voros A 1976 Ann. Inst. Henri Poincaré A 24 31
44. Berry M V 1977 J. Phys. A: Math. Gen. 10 2083 Voros A 1976 Ann. Inst. Henri Poincaré A 24 31
45. Kaplan L and Heller E J 1998 Physica D 121 1
46. Kaplan L and Heller E J 2000 Phys. Rev. E 62 409
47. Eckhardt B, Fishman S, Keating J, Agam O, Main J and Muller K 1995 Phys. Rev. E 52 5893 Bäcker A, Schubert R and Stifter P 1998 Phys. Rev. E 57 5425
48. Eckhardt B, Fishman S, Keating J, Agam O, Main J and Muller K 1995 Phys. Rev. E 52 5893 Bäcker A, Schubert R and Stifter P 1998 Phys. Rev. E 57 5425
49. Boasman P A and Keating J P 1995 Proc. R. Soc. A 449 629
50. Prosen T and Znidaric M 2002 J. Phys. A: Math. Gen. 35 1455 Prosen T and Seligman T H 2002 J. Phys. A: Math. Gen. 35 4707
51. Prosen T and Znidaric M 2002 J. Phys. A: Math. Gen. 35 1455 Prosen T and Seligman T H 2002 J. Phys. A: Math. Gen. 35 4707
52. Dahlqvist P 1999 J. Phys. A: Math. Gen. 32 7317 Rahav S and Fishman S 2002 Nonlinearity 15 1541
53. Dahlqvist P 1999 J. Phys. A: Math. Gen. 32 7317 Rahav S and Fishman S 2002 Nonlinearity 15 1541
54. Sepulveda M A, Tomsovic S and Heller E J 1992 Phys. Rev. Lett. 69 402 Vanicek J and Heller E J 2001 Phys. Rev. E 64 026215
55. Sepulveda M A, Tomsovic S and Heller E J 1992 Phys. Rev. Lett. 69 402 Vanicek J and Heller E J 2001 Phys. Rev. E 64 026215
56. Mehlig B and Kaplan L in preparation