Holomorphic quantization on the torus and finite quantum mechanics

Journal of Physics A: Mathematical and General

Volumn 29, Issue 21, 1996, Pages 6737-6745

  Athanasiu, G G ^a   Floratos, E G ^b   Nicolis, S ^c  

^a UNIVERSITY OF CRETE   (Greece)

^b INP   (Greece)

^c UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030486105     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/29/21/010     Document Type: Article

References (54)

1. Weyl H 1940 Algebraic Theory of Numbers (Annals of Mathematical Studies 1) (Princeton, NJ: Princeton University Press) Hardy G H and Wright E M 1978 An Introduction to the Theory of Numbers 5th edn (Oxford: Clarendon) Lang S 1970 Algebraic Number Theory (New York: Addison-Wesley)
2. Weyl H 1940 Algebraic Theory of Numbers (Annals of Mathematical Studies 1) (Princeton, NJ: Princeton University Press) Hardy G H and Wright E M 1978 An Introduction to the Theory of Numbers 5th edn (Oxford: Clarendon) Lang S 1970 Algebraic Number Theory (New York: Addison-Wesley)
3. Weyl H 1940 Algebraic Theory of Numbers (Annals of Mathematical Studies 1) (Princeton, NJ: Princeton University Press) Hardy G H and Wright E M 1978 An Introduction to the Theory of Numbers 5th edn (Oxford: Clarendon) Lang S 1970 Algebraic Number Theory (New York: Addison-Wesley)
4. Arnold V I 1978 Mathematical Methods of Classical Mechanics (Springer Graduate Texts in Mathematics 60) (Berlin: Springer) Arnold V I and Avez A 1968 Ergodic Problems of Classical Mechanics (New York: Benjamin)
5. Arnold V I 1978 Mathematical Methods of Classical Mechanics (Springer Graduate Texts in Mathematics 60) (Berlin: Springer) Arnold V I and Avez A 1968 Ergodic Problems of Classical Mechanics (New York: Benjamin)
6. Vivaldi F 1992 Geometry of linear maps over finite fields Nonlinearity 5 133
7. Hannay J and Berry M V 1980 Physica 1D 267 Berry M V 1987 Proc. R. Soc. A 473 183
8. Hannay J and Berry M V 1980 Physica 1D 267 Berry M V 1987 Proc. R. Soc. A 473 183
9. Balazs N L and Voros A 1986 Phys. Rep. C 143 109 Chirikov B V, Izrailev F M and Shepelyansky D 1988 Physica 33D 77 Ford J, Mantica G and Ristow G H 1991 Physica 50D 493 Leboeuf P and Voros A 1993 Quantum Chaos ed G Casati and B V Chirikov (Cambridge: Cambridge University Press)
10. Balazs N L and Voros A 1986 Phys. Rep. C 143 109 Chirikov B V, Izrailev F M and Shepelyansky D 1988 Physica 33D 77 Ford J, Mantica G and Ristow G H 1991 Physica 50D 493 Leboeuf P and Voros A 1993 Quantum Chaos ed G Casati and B V Chirikov (Cambridge: Cambridge University Press)
11. Balazs N L and Voros A 1986 Phys. Rep. C 143 109 Chirikov B V, Izrailev F M and Shepelyansky D 1988 Physica 33D 77 Ford J, Mantica G and Ristow G H 1991 Physica 50D 493 Leboeuf P and Voros A 1993 Quantum Chaos ed G Casati and B V Chirikov (Cambridge: Cambridge University Press)
12. Balazs N L and Voros A 1986 Phys. Rep. C 143 109 Chirikov B V, Izrailev F M and Shepelyansky D 1988 Physica 33D 77 Ford J, Mantica G and Ristow G H 1991 Physica 50D 493 Leboeuf P and Voros A 1993 Quantum Chaos ed G Casati and B V Chirikov (Cambridge: Cambridge University Press)
13. Sokoloff J B 1985 Phys. Rep. C 126 184
14. Cappelli A, Itzykson C and Zuber J-B 1987 Commun. Math. Phys. 113 1
15. Coste A and Gannon T 1994 Phys. Lett. 323B 316
16. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
17. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
18. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
19. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
20. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
21. Freund P G O and Witten E 1987 Phys. Lett. 199B 191 Ruelle Ph, Thiran E, Verstegen D and Weyers J 1989 J. Math. Phys. 30 2854 Meurice Y 1989 Int. J. Mod. Phys. A 4 5133; 1991 Commun. Math. Phys. 135 303; 1990 Phys. Lett. 245B 99 Brekke L and Freund, P G O 1993 p-adic numbers in physics Phys. Rep. C 233 1
22. Waldschmidt M, Moussa P, Luck J-M and Itzykson C (ed) 1992 From Number Theory to Physics (Les Houches Conf.) (Berlin: Springer)
23. Schröder M R S 1989 Number Theory in Science and Communications (Springer Series in Information Sciences) corr. 2nd printing (Berlin: Springer)
24. Lidl B and Niederreiter H 1984 Finite Fields and their Applications (Encyclopedia of Mathematics 20) (Cambridge: Cambridge University Press)
25. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
26. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
27. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
28. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
29. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
30. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
31. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
32. Bekenstein J 1980 Black hole thermodynamics Phys. Today; Do we understand black hole entropy? Preprint gr-qc/9409015', talk at 7th Marcel Grossmann Symposium on General Relativity 't Hooft G 1990 Nucl. Phys. B 335 138; 1990 Nucl. Phys. B 342 471 Susskind L, Thorlacius L and Uglum J 1993 Phys. Rev. D 49 3743 Polchinski J and Strominger A 1994 A possible resolution of the black hole information paradox Phys. Rev. D 50 7403 Kiem Y, Verlinde H and Verlinde E Black hole horizons and complementarity Preprint hep-th/9502074 Larsen F and Wilczek F Renormalization of black hole entropy and the gravitational coupling constant Preprint hep-th/9506006
33. Veneziano G 1986 Europhys. Lett. 2 199 Gross D J and Mende P 1987 Phys. Lett. 197B 129; 1988 Nucl. Phys. B 303 407. Amati D, Ciafaloni M and Veneziano G 1987 Phys. Lett. 197B 81 Konishi K, Paffuti G and Provero P 1990 Phys. Lett. 276B 276
34. Veneziano G 1986 Europhys. Lett. 2 199 Gross D J and Mende P 1987 Phys. Lett. 197B 129; 1988 Nucl. Phys. B 303 407. Amati D, Ciafaloni M and Veneziano G 1987 Phys. Lett. 197B 81 Konishi K, Paffuti G and Provero P 1990 Phys. Lett. 276B 276
35. Veneziano G 1986 Europhys. Lett. 2 199 Gross D J and Mende P 1987 Phys. Lett. 197B 129; 1988 Nucl. Phys. B 303 407. Amati D, Ciafaloni M and Veneziano G 1987 Phys. Lett. 197B 81 Konishi K, Paffuti G and Provero P 1990 Phys. Lett. 276B 276
36. Veneziano G 1986 Europhys. Lett. 2 199 Gross D J and Mende P 1987 Phys. Lett. 197B 129; 1988 Nucl. Phys. B 303 407. Amati D, Ciafaloni M and Veneziano G 1987 Phys. Lett. 197B 81 Konishi K, Paffuti G and Provero P 1990 Phys. Lett. 276B 276
37. Veneziano G 1986 Europhys. Lett. 2 199 Gross D J and Mende P 1987 Phys. Lett. 197B 129; 1988 Nucl. Phys. B 303 407. Amati D, Ciafaloni M and Veneziano G 1987 Phys. Lett. 197B 81 Konishi K, Paffuti G and Provero P 1990 Phys. Lett. 276B 276
38. Athanasiu G G and Floratos E G 1994 Nucl. Phys. B 425 343.
39. Balian R and Itzykson C 1986 C. R. Acad. Sci., Paris I 303 773
40. Cartier P 1966 Quantum Mechanical Commutation Relations and Theta Functions (Proc. Symp. Pure Mathematics 9) Algebraic-Discontinuous Groups (Providence, RI: American Mathematical Society)
41. Weyl H 1931 The Theory of Groups and Quantum Mechanics (New York: Dover) Schwinger J 1960 Proc. Nat; Acad. Sci. 46 257, 544, 883
42. Weyl H 1931 The Theory of Groups and Quantum Mechanics (New York: Dover) Schwinger J 1960 Proc. Nat; Acad. Sci. 46 257, 544, 883
43. Mumford D 1986 Tata Lectures on Theta vols I-III (New York: Birkhäuser)
44. Weil A 1964 Acta Math. 111 143
45. Tanaka S 1966 Osaka J. Math. 3 229
46. Tanaka S 1967 Osaka J. Math. 4 65
47. Evans R J 1986 Hermite character sums Pacific J. Math. 122 357
48. Auslander S and Tolmieri P 1979 Bull. Am. Math. Soc. 1 847 Berndt B C and Evans R J 1981 Bull. Am. Math. Soc. 5 107
49. Auslander S and Tolmieri P 1979 Bull. Am. Math. Soc. 1 847 Berndt B C and Evans R J 1981 Bull. Am. Math. Soc. 5 107
50. Mehta M L 1989 Matrix Theory (Paris: Editions de Physique)
51. Feynman R P 1986 Quantum mechanical computers Found. Phys. 16 507 Deutsch D 1989 Quantum computational networks Proc. R. Soc. A 425 73 Loyd S 1994 Envisioning a quantum supercomputer Science 263 695
52. Feynman R P 1986 Quantum mechanical computers Found. Phys. 16 507 Deutsch D 1989 Quantum computational networks Proc. R. Soc. A 425 73 Loyd S 1994 Envisioning a quantum supercomputer Science 263 695
53. Feynman R P 1986 Quantum mechanical computers Found. Phys. 16 507 Deutsch D 1989 Quantum computational networks Proc. R. Soc. A 425 73 Loyd S 1994 Envisioning a quantum supercomputer Science 263 695
54. Shor P W 1994 Algorithms for quantum computation: discrete logarithms and factoring Proc. IEEE Computer Society Press (November) p 124