Interference of probabilities and number field structure of quantum models

Annalen der Physik (Leipzig)

Volumn 12, Issue 10, 2003, Pages 575-585

  Khrennikov, Andrei ^a  

^a LINNAEUS UNIVERSITY   (Sweden)

Author keywords

Complex; Hyperbolic numbers; Interference of probabilities; Number field structure; P adic; Quantum probability; Real

Indexed keywords

ELEMENTARY PARTICLES; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY;

HYPERBOLIC NUMBER; NUMBER FIELD STRUCTURE; QUANTUM PROBABILITY;

QUANTUM THEORY;

EID: 0345171480     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/andp.200310027     Document Type: Article

References (31)

1. P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1995).
2. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J., 1955).
3. D. Finkelstein, J. M. Jauch, S. Schiminovich, and D. Speiser, Foundations of quaternion quantum mechanics, J. Math. Phys., 3, 207 (1962).
4. E. Beltrametti and G. Cassinelli, The Logic of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1981).
5. E. Beltrametti and G. Cassinelli, Quantum mechanics and p-adic numbers Found. Phys. 2, 1-7 (1972).
6. K. Gurlebeck and W. Sproessig, Quaternionic and Clifford Calculus for Physicists and Engineers (John Wiley & Sons, New York, 1998).
7. I. V. Volovich, p-adic string, Class. Quantum Gravity 4 83-87 (1987).
8. P. G. O. Freund and E. Witten, Adelic string amplitudes, Phys. Lett. B 199 191-195 (1987).
9. P. H. Frampton and Y. Okada, p-adic string N-point function, Phys. Rev. Lett. 60, 484-486 (1988).
10. V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov, p-adic Numbers in Mathematical Physics (World Scientific Publ., Singapore, 1994).
11. A. Yu. Khrennikov, p-adic Valued Distributions in Mathematical Physics (Kluwer Academic Publishers, Dordrecht, 1994).
12. V. S. Vladimirov and I. V. Volovich, Superanalysis, 1. Differential calculus, Teor. Mat. Fiz. 59(1), 3-27 (1984).
13. V. S. Vladimirov and I. V. Volovich, Superanalysis, 2. Integral calculus, Teor. Mat. Fiz. 60(2), 169-198 (1984).
14. A. Yu. Khrennikov, Superanalysis (Kluwer Academic Publishers, Dordrect/Bostob/London, 1999).
15. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1951).
16. D. Bohm and B. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Mechanics (Routledge and Kegan Paul, London, 1993).
17. J. von Neumann and G. Birkhoff, Ann. Math. 37, 823 (1936).
18. D. Finkelstein, J. M. Jauch, S. Schiminovich, and D. Speiser, J. Math. Phys. 3, 207 (1962).
19. W. Heisenberg, Physical Principles of Quantum Theory, (Chicago Univ. Press, 1930).
20. A. N. Kolmogoroff, (Springer Verlag, Berlin, 1933); Grundbegriffe der Wahrscheinlichkeitsrechnung Reprint: Foundations of the Probability Theory (Chelsea Publ. Comp., New York, 1956).
21. A. N. Shiryayev, Probability (Springer, Berlin-Heidelberg-New York, 1984).
22. A. Yu. Khrennikov, Ensemble fluctuations and the origin of quantum probabilistic rule, J. Math. Phys. 43(2), 789-802 (2002).
23. A. Yu. Khrennikov, Linear representations of probabilistic transformations induced by context transitions, J. Phys. A, Math. Gen. 34, 9965-9981 (2001).
24. L. Accardi, Urne e Camaleoni: Dialogo sulla realta, le leggi del caso e la teoria quantistica (Il Saggiatore, Rome, 1997); English translation to be published by Kluwer Academic Publ.
25. L. Ballentine, Interpretations of probability and quantum theory, in Proceedings of the Conf. "Foundations of Probability and Physics", Växjö, Sweden, 2000, Quantum Probability and White Noise Analysis 13, edited by A. Yu. Khrennikov, (WSP, Singapore, 2001), pp. 71-84.
26. W. M. De Muynck, Interpretations of quantum mechanics, and interpretations of violations of Bell's inequality, in Proceedings of the Conf. "Foundations of Probability and Physics", Växjö, Sweden, 2000, Quantum Probability and White Noise Analysis 13, edited by A. Yu. Khrennikov, (WSP, Singapore, 2001), pp. 95-114.
27. U. Bose and H. Rauch (eds.), Neuron Interferometry (Clarendon Press, Oxford, 1979)
28. W. Schikhov, Ultrametric Calculus (Cambridge Univ. Press, Cambridge, 1984).
29. S. Albeverio and A. Yu. Khrennikov, J. Phys. A 29, 5515-5527 (1996).
30. A. Yu. Khrennikov, Non-Archimedean analysis: Quantum Paradoxes, Dynamical Systems and Biological Models (Kluwer Acad. Publishers, Dordrecht/Boston/London, 1997).
31. I. Ya. Aref'eva, B. Dragovich, P. H. Frampton, and I. V. Volovich, Int. J. Mod. Phys. A 6, 4341-4358 (1991).