Complex probabilities on RN as real probabilities on CN and an application to path integrals

Physical Review Letters

Volumn 89, Issue 24, 2002, Pages 2402011-2402014

  Weingarten, Don ^a  

^a IBM RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FUNCTIONS; INTEGRAL EQUATIONS; PROBABILITY;

PATH INTEGRALS;

QUANTUM THEORY;

EID: 0037049521     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. John Klauder, in Recent Developments in High-Energy Physics, edited by H. Mitter and C.B. Lang (Springer, Vienna, 1983); Phys. Rev. A 29, 2036 (1984).
2. John Klauder, in Recent Developments in High-Energy Physics, edited by H. Mitter and C.B. Lang (Springer, Vienna, 1983); Phys. Rev. A 29, 2036 (1984).
3. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
4. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
5. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
6. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
7. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
8. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
9. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
10. J. Ambjorn, M. Fiensburg, and C. Petersen, Phys. Lett. 159B, 335 (1985); J.R. Klauder and W.P. Petersen, J. Stat. Phys. 39, 53 (1985); J. Ambjorn and S.K. Yang, Phys. Lett. 165B, 140 (1985); J. Ambjorn, M. Flensburg, and C. Peterson, Nucl. Phys. B275[FS17], 375 (1986); B. Söderberg, Nucl. Phys. B295[FS21], 396 (1988); L.L. Salcedo, Phys. Lett. B 304, 125 (1993); S. Lee, Nucl. Phys. B41[FS], 827 (1994); H. Gausterer, J. Phys. A 27, 1325 (1994).
11. L.L. Salcedo, J. Math. Phys. (N.Y.) 38, 1710 (1997).
12. I am grateful to L.L. Salcedo for suggesting the proof of the existence of p(r) for N = 1.
13. N.I. Akhiezer, The Classical Moment Problem (Hafner, New York, 1965).
14. C. Berg, Proc. Symp. Appl. Math. 37, 110 (1987).
15. A.A. Migdal, Soy. Phys. Usp. 29, 389 (1986).
16. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).
17. D. Weingarten, Nuovo Cimento Soc. Ital. Fis. 22B, 293 (1974).
18. D. Weingarten, Neils Bohr institute Report No. NBI-HE-73-3, 1973.
19. R.B. Griffiths, J. Stat. Phys. 36, 219 (1984); R. Omnes, J. Stat. Phys. 53, 893 (1988); M. Gell-Mann and J.B. Hartle, in Complexity, Entropy, and the Physics of Information, edited by W. Zurek (Addison-Wesley, Reading, MA, 1990), p. 425.
20. R.B. Griffiths, J. Stat. Phys. 36, 219 (1984); R. Omnes, J. Stat. Phys. 53, 893 (1988); M. Gell-Mann and J.B. Hartle, in Complexity, Entropy, and the Physics of Information, edited by W. Zurek (Addison-Wesley, Reading, MA, 1990), p. 425.
21. R.B. Griffiths, J. Stat. Phys. 36, 219 (1984); R. Omnes, J. Stat. Phys. 53, 893 (1988); M. Gell-Mann and J.B. Hartle, in Complexity, Entropy, and the Physics of Information, edited by W. Zurek (Addison-Wesley, Reading, MA, 1990), p. 425.
22. S. Goldstein, Phys. Today 51, No. 3, 42 (1998); 51, No. 4, 38 (1998).
23. S. Goldstein, Phys. Today 51, No. 3, 42 (1998); 51, No. 4, 38 (1998).