Quantum theory without Hilbert spaces

Foundations of Physics

Volumn 31, Issue 11, 2001, Pages 1545-1580

  Anastopoulos, C ^a  

^a Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035729703     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012690715414     Document Type: Article

References (49)

1. J. von Neumann, The Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1996).
2. H. Everett, "Relative state formulation of quantum mechanics," Rev. Mod. Phys. 29, 454 (1957).
3. B. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1973).
4. R. B. Griffiths, "Consistent histories and the interpretation of quantum mechanics," J. Stat. Phys. 36, 219 (1984).
5. R. Omnès, "Logical reformulation of quantum mechanics: I Foundations, J. Stat. Phys. 53, 893 (1988); The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994); "Consistent interpretations of quantum mechanics," Rev. Mod. Phys. 64, 339 (1992).
6. R. Omnès, "Logical reformulation of quantum mechanics: I Foundations, J. Stat. Phys. 53, 893 (1988); The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994); "Consistent interpretations of quantum mechanics," Rev. Mod. Phys. 64, 339 (1992).
7. R. Omnès, "Logical reformulation of quantum mechanics: I Foundations, J. Stat. Phys. 53, 893 (1988); The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994); "Consistent interpretations of quantum mechanics," Rev. Mod. Phys. 64, 339 (1992).
8. M. Gell-Mann and J. B. Hartle, "Quantum mechanics in the light of quantum cosmology," in Complexity, Entropy and the Physics of Information, W. Zurek, ed. (Addison Wesley, Reading, 1990); "Classical equations for quantum systems," Phys. Rev. D 47, 3345 (1993).
9. M. Gell-Mann and J. B. Hartle, "Quantum mechanics in the light of quantum cosmology," in Complexity, Entropy and the Physics of Information, W. Zurek, ed. (Addison Wesley, Reading, 1990); "Classical equations for quantum systems," Phys. Rev. D 47, 3345 (1993).
10. J. B. Hartle, "Spacetime quantum mechanics and the quantum mechanics of spacetime," in Proceeding on the 1992 Les Houches School, Gravitation and Quantisation, 1993.
11. J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195 (1964).
12. S. Kochen and R. P. Speecker, "The problem of hidden variables in quantum mechanics," J. Math. Mech. 17, 59 (1967).
13. A. Aspect, J. Dalibard, and G. Roger, "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: A N's Inequalities," Phys. Rev. Lett. 49, 91 (1982).
14. D. Bohm, "A suggested interpretation of the quantum theory in terms of hidden variables," Phys. Rev. 85, 166 (1952).
15. D. Bohm and B. J. Hiley, The Undivided Universe (Routledge, London, 1993).
16. Y. Aharonov and D. Bohm, "Significance of electromagnet potentials in the quantum theory," Phys. Rev. 115, 485, (1959).
17. C. Anastopoulos and K. Sovvidou, "Quantum mechanical histories and the berry phase," quant-ph/0007093.
18. K. Savvidou, "The action operator in continuous time histories," J. Math. Phys. 40, 5657 (1999).
19. J. J. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, Reading, 1968).
20. E. B. Davies, Quantum Theory of Open System (Academic, London, 1976).
21. P. Busch, M. Grabowski, and P. J. Lahti, Operational Quantum Physics (Springer, Berlin, 1995).
22. R. G. Chambers, Phys. Rev. Lett. 5, 1 (1960).
23. J. Samuel and R. Bhandari, "General setting for Berry phase," Phys. Rev. Lett. 60, 2339 (1988).
24. D. Suter, K. T. Mueller, and A. Pines, "Study of the Aharonov-Anandan quantum phase by NMR Interferometry," Phys. Rev. Lett. 60, 1218 (1988).
25. F. Dowker and A. Kent, "On the consistent histories approach to quantum mechanics," J. Stat. Phys. 82, 1575 (1996).
26. A. Kent, "Consistent sets yield contradictory inferences in quantum theory," Phys. Rev. Lett. 78, 2874 (1997).
27. R. Griffiths and J. B. Hartle, "Comment on consistent sets yield contrary inferences in quantum theory," Phys. Rev. Lett. 81, 1981 (1998).
28. R. Griffiths, "Consistent quantum counterfactuals," Phys. Rev. A 60, 5 (1999).
29. C. J. Isham, "Topos theory and consistent histories: the internal logic of the set of all consistent sets," Int. J. Theor. Phys. 36, 785 (1997).
30. R. D. Sorkin, "Quantum mechanics as quantum measure theory," Mod. Phys. Lett. A 9, 3119 (1994).
31. R. D. Sorkin, "Quantum measure theory and its interpretation," in Quantum Classical Correspondence, D. H. Feng and B. L. Huy, eds. (International Press, Cambridge, MA, 1997).
32. C. Anastopoulos, "Selection of preferred consistent sets," Int. J. Theor. Phys. 37, 2261 (1998).
33. C. J. Isham, "Quantum logic and the histories approach to quantum theory," J. Math. Phys. 35, 2157 (1994).
34. C. J. Isham and N. Linden, "Continuous histories and the history group in generalised quantum theory," J. Math. Phys. 36, 5392 (1995).
35. C. J. Isham and N. Linder, "Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory," J. Math. Phys. 35, 5452 (1994).
36. E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, 1985).
37. J. S. Schwinger, "Brownian motion of a quantum oscillator," J. Math. Phys. 2, 407 (1961).
38. L. V. Keldysh, "Diagram technique for nonequilibrium processes," Zh. Eksp. Teor. Fiz. 47, 1515 (1964).
39. C. Anastopoulos, "Continuous-time histories: observables, probabilities, phase space structure and the classical limit," quant-ph/0008052.
40. J. Klauder, "The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbers," Ann. Phys. 11, 123 (1959).
41. A. Khrennikov, "Einstein and Bell, von Mises and Kolmogorov: Reality and locality, frequency and probability," quant-ph/0006016.
42. E. C. G. Stueckelberg, "Quantum theory in real Hilbert space," Helv. Phys. Acta 33, 727 (1960).
43. A. Kent, "Quasiclassical dynamics in a closed quantum system," Phys. Rev. A 54, 4670 (1996).
44. D. M. Greenberger, M. A. Home, and A. Zeilinger, "Going beyond Bell's theorem" in Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, Dordrecht, 1989).
45. N. J. Woodhouse, Geometric Quantization (Oxford University Press, Oxford, 1992).
46. C. J. Isham, "Topological and global aspects of quantum theory," in Proceedings of the 1983 Les Houches School, Relativity, Groups and Topology II.
47. G. S. Agarwal, "Perspective of Einstein-Podolsky-Rosen spin correlations in the phase space formulation for arbitrary values of the spin," Phys. Rev. A 47, 4608 (1993).
48. C. Isham, N. Linden, K. Savvidou, and S. Schreckenberg, "Continuous time and consistent histories," J. Math. Phys. 37, 2261 (1998).
49. K. Savvidou, "Continuous time in consistent histories," gr-qc/9912076.