An inverse problem in quantum field theory and canonical correlation functions

Journal of the Mathematical Society of Japan

Volumn 51, Issue 2, 1999, Pages 337-369

  Hirokawa, Masao ^a,b  

^a HITACHI LTD   (Japan)

^b OKAYAMA UNIVERSITY   (Japan)

Author keywords

Finite temperature; Infinite volume limit; Inverse problem; Quantum field theory; Rotating wave approximation

Indexed keywords

EID: 0040705438     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/05120337     Document Type: Article

References (34)

1. J.-P. Antoine and W. Karwowski, Partial *-algebra of closed linear operators in Hilbert space, Publ. RIMS, Kyoto Univ., 21(1985), 205-236.
2. J.-P. Antoine and W. Karwowski, Partial *-algebra of closed linear operators in Hilbert space, Add./Err. Kyoto Univ. 22 (1986), 507-511.
3. J.-P. Antoine and F. Mathot, Partial ^-algebra of closed linear operators and their commutants I. General structure, Ann. Inst. H. Poincare, 46 (1987), 299-324.
4. J.-P. Antoine, A. Inoue and C. Trapani, Partial p-algebra of closable operators I. The basic theory and the abelian case, Publ. RIMS, Kyoto Univ., 26 (1990), 359-395.
5. A. Arai, Spectral analysis of a quantum harmonic oscillator coupled to infinite many scalar bosons, J. Math. Anal. Appl.140 (1989), 270-288.
6. A. Arai, Long-time behavior of two-point functions of a quantum harmonic oscillator interacting with bosons, J. Math. Phys. 30 (1989), 1277-1288.
7. A. Arai, Path integral representation of the index of Kahler-Dirac operators on an infinite dimensional manifold, J. Func. Anal.82 (1989), 330-369.
8. A. Arai and M. Hirokawa, On the Existence and Uniqueness of Ground States of a Generalized Spin-Boson Model, J. Funct. Anal., 151(1997), 455-503.
9. O. Bratteli and D. W. Robinson, Operator algebras and Quantum Statistical Mechanics II, SpringerVerlag, New York, 1981.
10. I. Braun, Irreversible behavior of a quantum harmonic oscillator coupled to a heat bath, Physica, 129A (1985), 262-301.
11. H. Ezawa and A. Arai, Quantum fields theory and statistical mechanics, Nihon Hyoron Sha, Tokyo, 1988 (in Japanese).
12. G. W. Ford and M. Kac, On the Quantum Langevin equation, J. Stat. Phys., 46 (1987), 803-810.
13. G. W. Ford, J. T. Lewis and R. F. O’Connell, Quantum Langevin equation, Phys. Rev. A, 37 (1988), 4419-4428.
14. J. Glimm and A. Jaffe, Singular perturbations of self-adjoint operators, Comm. Pure Appl. Math., 22 (1969), 401-414.
15. 2 quantum field theory without cutoffs I. Phys. Rev.176 (1968), 1945-1951.
16. 4)2 quantum field theory without cutoffs II. The field operators and the approximate vacuum, Ann. Math. 91(1970), 362-401.
17. H. Haken, Laser Theory, in “Encyclopedia of Physics,” Vol. XXV/2c, Springer-Verlag, Berlin, 1970.
18. M. Hirokawa, Rigorous construction of Liouville spaces and thermo field dynamics for bosonic systems in mathematics, Ann. Phys. (N.Y.) 223 (1993), 1-36.
19. M. Hirokawa, Mori’s memory kernel equation for a quantum harmonic oscillator coupled to RWA-oscillator, Ann. Phys. (N.Y.) 224 (1993), 301-341.
20. M. Hirokawa, Mori’s memory kernel equation in equilibrium quantum systems in finite volume, Ann. Phys. (N.Y.) 229 (1994), 354-383.
21. Errata, Ann. Phys. (N.Y.) 235 (1994), 240-241.
22. M. Hirokawa, A mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in Mori’s theory, Ann. Phys. (N.Y.) 234 (1994), 185-210.
23. M. Hirokawa, General properties between the canonical correlation and independent-oscillator model on a partial *-algebra, J. Math. Phys. 37 (1996), 121-146.
24. S. S. Horuzhy, Introduction to algebraic quantum field theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1990.
25. K. Lindenberg and J. West, Statistical properties of quantum systems: The linear oscillator, Phys. Rev. A, 30 (1984), 568-582.
26. H. Mori, Transport, collective motion and Brownian motion, Prog. Theo. Phys. 33 (1965), 423-455.
27. H. Mori, A continued-fraction representation of the time-correlation functions, Prog. Theo. Phys. 34 (1965), 399-416.
28. J. Naudts, A. Verbeure and R. Weder, Linear response theory and the KMS condition, Comm. Math. Phys. 44 (1975), 87-99.
29. Y. Okabe, KMO-Langevin equation and fluctuation-dissipation theorem (I), Hokkaido Mathematical Journal15 (1986), 163-216.
30. M. Reed and B. Simon, Methods of Modern Mathematical Physics Vol I: Functional Analysis, Academic Press, New York, 1980.
31. M. Reed and B. Simon, Methods of Modern Mathematical Physics Vol II: Fourier Analysis, SelfAdjointness, Academic Press, New York, 1975.
32. M. Reed and B. Simon, Methods of Modern Mathematical Physics Vol IV: Analysis of Operators, Self-Adjointness, Academic Press, New York, 1978.
33. Y. Takahashi, Quantum Field Theory I for Condensed Matter Physicists, Baihukan, Tokyo, 1984 (in Japanese).
34. T. Yamanouchi, Quantum Mechanics, Baihukan, Tokyo, 1984 (in Japanese).