HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 14 (1955) > Number 4
| Next Article >

Prog. Theor. Phys. Vol. 14 No. 4 (1955) pp. 351-378

[ Full Text PDF : FREE ACCESS (1842K) ]

A New Approach to Quantum-Statistical Mechanics

Takeo Matsubara

Research Institute for Fundamental Physics, Kyoto University

(Received August 1, 1955)

Abstract:

A new method of calculating the grand partition function of many-body system is developed, adopting extensively the technique of calculus in quantum field theory. It is shown that the grand partition function, which is a trace of the density matrix expressed in terms of field operators, can be evaluated in a way almost parallel with the evaluation of the vacuum expectation value of the S-matrix in quantum field theory, provided that appropriate modifications in notation and definitions are made. As an example, the method is applied to electron-phonon system. Further, basing on this new formalism, various non-perturbational methods are discussed.


URL : http://ptp.ipap.jp/link?PTP/14/351/
DOI : 10.1143/PTP.14.351

[ Full Text PDF : FREE ACCESS (1842K) ] Citation:

References:

  1. R. Kubo, Phys. Rev. 87 (1952), 568[APS].
  2. M. R. Schafroth, Helv. Phys. Acta. 24 (1951), 645.
  3. G. V. Chester, Phys. Rev. 93 (1954), 606[APS]; ibid. 94 (1954), 246[APS].
  4. R. P. Feynman, Phys. Rev. 91 (1953), 1291[APS].
  5. M. H. Friedman and S. T. Butler, Phys. Rev. 98 (1955), 287[APS]; ibid. 98 (1955), 294[APS].
  6. H. Ichimura, Prog. Theor. Phys. 11 (1954), 374[PTP]; ibid. 11 (1954), 385[PTP]; ibid. 11 (1954), 519[PTP].
  7. F. J. Dyson, Phys. Rev. 75 (1949), 486[APS].
  8. F. Nakano and Y. Kitano, Prog. Theor. Phys. 9 (1953), 370[PTP].
  9. G. C. Wick, Phys. Rev. 80 (1950), 268[APS].
  10. J. L. Anderson, Phys. Rev. 94 (1954), 703[APS].
  11. H. Fröhlich, Proc. R. Soc. A 223 (1954), 296.
    S. Nakajima, Busseiron Kenkyu (in Japanese) 65 (1953), 116.
  12. M. Born and H. S. Green, Proc. R. Soc. A 188 (1946), 10.
  13. G. Kirkwood, J. Chem. Phys. 14 (1946), 180[CrossRef].
  14. J. Schwinger, Proc. Nat. Acad. Sci. U. S. 37 (1951), 452.
  15. S. F. Edwards and Peierls, Proc. R. Soc. A 224 (1954), 24.
  16. T. Kinoshita and Y. Nambu, Phys. Rev. 94 (1954), 598[APS].
  17. J. Bardeen, Phys. Rev. 81 (1951), 829[APS].
  18. H. Fröhlich, Proc. R. Soc. A 223 (1954), 296.
    C. G. Kuper, Proc. R. Soc. A 227 (1955), 214.
  19. W. Macke, Z. f. Naturforsh. a 5 (1950), 192.

Citing Article(s) :

  1. Journal of the Physical Society of Japan 67 (1998) pp. 2430-2438 :
    Landauer Type Approach to Electron Conduction in One-Dimensional Systems and Interaction Effects
    Arisato Kawabata
  2. Journal of the Physical Society of Japan 72 (2003) pp. 3097-3105 :
    Molecular Orbital Theory: Spinor Representation
    Shigeyuki Aono
  3. Journal of the Physical Society of Japan 77 (2008) 024711 (9 pages) :
    Quantum Transport Equation for Bloch Electrons in Electromagnetic Fields
    Takafumi Kita and Hiromasa Yamashita
  4. Progress of Theoretical Physics Vol. 16 No. 2 (1956) pp. 71-94 :
    On the Quantum Mechanics-like Description of the Theories of the Brownian Motion and Quantum Statistical Mechanics
    Nobuhiko Saitô and Mikio Namiki
  5. Progress of Theoretical Physics Vol. 21 No. 3 (1959) pp. 389-408 :
    Electrostatic Interactions in an Electron-Ion Gas at High Density
    Toshiyuki Nishiyama
  6. Progress of Theoretical Physics Vol. 22 No. 2 (1959) pp. 213-226 :
    Giant Cluster Expansion Theory and Its Application to High Temperature Plasma
    Ryuzo Abe
  7. Progress of Theoretical Physics Vol. 22 No. 3 (1959) pp. 466-468 :
    Green Function Method in Quantum-Statistics
    Hideo Kanazawa and Mitsuo Watabe
  8. Progress of Theoretical Physics Vol. 23 No. 3 (1960) pp. 408-425 :
    Green Function Method for Electron Gas. I
    Hideo Kanazawa and Mitsuo Watabe
  9. Progress of Theoretical Physics Vol. 23 No. 4 (1960) pp. 629-661 :
    One-Particle Motions in Many-Particle Systems and the Optical Model in Nuclear Reactions
    Mikio Namiki
  10. Progress of Theoretical Physics Vol. 24 No. 2 (1960) pp. 457-459 :
    de Haas-van Alphen Effect and Coulomb Interaction
    Hiroshi Ichimura and Setsuko Tanaka
  11. Progress of Theoretical Physics Vol. 25 No. 3 (1961) pp. 315-326 :
    Quantum Statistics of Interacting Electron Gas in a Strong Magnetic Field
    Hiroshi Ichimura and Setsuko Tanaka
  12. Progress of Theoretical Physics Vol. 25 No. 5 (1961) pp. 735-742 :
    Quantum Statistical Analogue of Ward's Identity
    Keiji Watanabe, Osamu Kamei and Hiroshi Ezawa
  13. Progress of Theoretical Physics Vol. 25 No. 6 (1961) pp. 964-980 :
    An Expansion Theorem for the Elecric Conductivity of Metals. I
    Takeo Izuyama
  14. Progress of Theoretical Physics Vol. 26 No. 4 (1961) pp. 453-469 :
    Renormalization of the Partition Function in the Relativistic Statistical Mechanics of Electron Gas
    Keiji Watanabe
  15. Progress of Theoretical Physics Vol. 28 No. 3 (1962) pp. 407-423 :
    On the Singularity of t-Matrix of Interacting Fermion Systems
    Shuichiro Yamasaki
  16. Progress of Theoretical Physics Vol. 28 No. 4 (1962) pp. 690-710 :
    On the Green's Functions of the Heisenberg Spin Systems
    Kyozi Kawasaki and Hazime Mori
  17. Progress of Theoretical Physics Vol. 28 No. 6 (1962) pp. 951-958 :
    Infrared Divergencies in Statistical Mechanics of Electron Plasma
    Keiji Watanabe
  18. Progress of Theoretical Physics Vol. 30 No. 6 (1963) pp. 772-785 :
    On the Electron-Phonon Interaction in Normal Metals. II
    Sadao Nakajima and Mitsuo Watabe
  19. Progress of Theoretical Physics Vol. 31 No. 6 (1964) pp. 1160-1162 :
    Definition of Normal Product and Wick's Theorem in Statistical Mechanics
    Masanao Kitamura
  20. Progress of Theoretical Physics Vol. 39 No. 5 (1968) pp. 1100-1120 :
    Cluster Expansion for Degenerate Bose Fluids
    Tohru Morita
  21. Progress of Theoretical Physics Vol. 41 No. 1 (1969) pp. 60-87 :
    Long-Distance Behaviors of the Pair Distribution Function of Degenerate and Non-Degenerate Bose Fluids
    Tohru Morita and Hiroaki Hara
  22. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 590-603 :
    Longitudinal Spin Pair Correlation in Ferro- and Antiferromagnets with Uniaxial Anisotropy
    Hideho Tanaka and Kensuke Tani
  23. Progress of Theoretical Physics Vol. 43 No. 3 (1970) pp. 647-659 :
    Behavior of Reduced Density Matrices of the Ideal Fermi Gas
    Hiroaki Hara
  24. Progress of Theoretical Physics Vol. 45 No. 5 (1971) pp. 1437-1457 :
    Long-Distance Behavior of the Pair Distribution Fnction of Hard-Sphere Fermi Gases
    Hiroaki Hara and Tohru Morita
  25. Progress of Theoretical Physics Vol. 46 No. 3 (1971) pp. 675-687 :
    Frequency Shift and Damping Constant of Spin Waves in a Heisenberg Ferrimagnet with Uniaxial Anisotropy
    Makoto Takemura and Kensuke Tani
  26. Progress of Theoretical Physics Vol. 46 No. 3 (1971) pp. 757-775 :
    Microscopic Theory of Thermal Conductivity in an Electron-Phonon System
    Yoshiyuki Ono
  27. Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 146-152 :
    Remarks on Statistical Mechanics of Interacting Systems
    Akira Ishihara and Yasushi Takahashi
  28. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 764-793 :
    Macroscopic Collective Excitations Associated with Phase Changes
    Koichiro Matsuno
  29. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 841-860 :
    Longitudinal Conductivity Sum Rule
    Takeo Izuyama
  30. Progress of Theoretical Physics Vol. 51 No. 1 (1974) pp. 26-42 :
    Theory of Optical Band Shape for A1g → T1u Transition. I
    Keiichiro Nasu and Tadanobu Kojima
  31. Progress of Theoretical Physics Vol. 51 No. 3 (1974) pp. 920-944 :
    Super-Quantization. II
    Susumu Okubo
  32. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 344-346 :
    Critical Dynamics in Bose Systems
    Masuo Suzuki and Fumihiko Tanaka
  33. Progress of Theoretical Physics Vol. 52 No. 4 (1974) pp. 1135-1145 :
    Quantum Effect, Critical Dynamics and One-Particle Excitation in 1/n Expansion. I
    Ryuzo Abe
  34. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1463-1472 :
    Quantum Effect, Critical Dynamics and One-Particle Excitation in 1/n Expansion. II
    Ryuzo Abe and Shinobu Hikami
  35. Progress of Theoretical Physics Vol. 53 No. 1 (1975) pp. 97-110 :
    On the Critical Dynamics in Bose Systems and the Time-Dependent Ginzburg-Landau Model
    Masuo Suzuki
  36. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1572-1583 :
    The Finite Temperature Nucleon Matter. I
    Masayoshi Kiguchi
  37. Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 249-258 :
    Supersymmetry and Scale-Dependent Analysis
    Minoru Ikeda
  38. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 599-602 :
    Thermo Field Dynamics in Interaction Representation
    H. Matsumoto, Y. Nakano, H. Umezawa, F. Mancini and M. Marinaro
  39. Progress of Theoretical Physics Vol. 73 No. 2 (1985) pp. 434-455 :
    Two-Loop Finite Temperature Effective Potential. I
    Yasushi Fujimoto, Robert Grigjanis and Randy Kobes
  40. Progress of Theoretical Physics Vol. 73 No. 5 (1985) pp. 1245-1257 :
    Behavior of Supersymmetry at Finite Temperature
    Shoichi Midorikawa
  41. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1320-1341 :
    A. Microscopic Theory of Superfluids. III
    Shuichiro Yamasaki
  42. Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1105-1123 :
    Two-Loop Finite Temperature Effective Potential with Fermion
    Yasushi Fujimoto and Robert Grigjanis
  43. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 311-314 :
    Screening Effect in Relativistic QED Plasma
    Shoichi Midorikawa and Yoshio Yamaguchi
  44. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1450-1462 :
    The Thirring Model at Finite Temperature and Density
    Hiroshi Yokota
  45. Progress of Theoretical Physics Vol. 85 No. 2 (1991) pp. 381-390 :
    The Anomalous Magnetic Moment of an Electron at Finite Temperature
    Tetsuo Yabuki and Akira Kanazawa
  46. Progress of Theoretical Physics Vol. 93 No. 6 (1995) pp. 987-1012 :
    Mean-Field Theory of Fluid-Solid Transition of Fermion Systems
    Koichi Takahashi
  47. Progress of Theoretical Physics Vol. 97 No. 5 (1997) pp. 709-737 :
    Developments and Outlook of Statistical Physics at the Turn of the Century
    Akira Isihara
  48. Progress of Theoretical Physics Vol. 99 No. 6 (1998) pp. 1069-1083 :
    Non-Perturbative Approach to the Effective Potential of the λφ4 Theory at Finite Temperature
    Tomohiro Inagaki, Kenzo Ogure and Joe Sato
  49. Progress of Theoretical Physics Vol. 106 No. 1 (2001) pp. 131-147 :
    The Auxiliary Mass Method beyond the Local Potential Approximation
    Kenzo Ogure and Joe Sato
  50. Progress of Theoretical Physics Vol. 106 No. 3 (2001) pp. 603-611 :
    Phase Diagram of the Abelian Higgs Model Using the Auxiliary Mass Method
    Kenzo Ogure
  51. Progress of Theoretical Physics Vol. 114 No. 6 (2005) pp. 1153-1161 :
    Space-Time Dependence of the BCS Order Parameter in Non-Equilibrium Systems
    Tadashi Toyoda
  52. Progress of Theoretical Physics Vol. 117 No. 3 (2007) pp. 415-429 :
    Gauge Covariant Formulation of the Wigner Representation through Deformation Quantization
    Naoyuki Sugimoto, Shigeki Onoda and Naoto Nagaosa
  53. Progress of Theoretical Physics Vol. 121 No. 3 (2009) pp. 577-591 :
    Variational Approach to the Chiral Phase Transition in the Linear Sigma Model
    Yasuhiko Tsue and Kazuki Matsuda
  54. Progress of Theoretical Physics Vol. 123 No. 4 (2010) pp. 581-658 :
    Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
    Takafumi Kita
  55. Progress of Theoretical Physics Vol. 123 No. 6 (2010) pp. 1013-1028 :
    First-Order Quark-Hadron Phase-Transition in a NJL-Type Model for Nuclear and Quark Matter
    Yasuhiko Tsue, João da Providência, Constança Providência and Masatoshi Yamamura
  56. Progress of Theoretical Physics Supplement No.80 (1984) pp. 19-25 :
    Diagrammatic Expansion in Condensed Matter Physics
    Ryuzo Abe
  57. Progress of Theoretical Physics Supplement No.80 (1984) pp. 26-39 :
    Methods of Quantum Field Theory in Condensed Matter Physics
    Hiroomi Umezawa
  58. Progress of Theoretical Physics Supplement No.80 (1984) pp. 62-75 :
    Methods of Dynamical Lie Algebra for Many Fermion Green Functions
    Joseph L. Birman and Allan I. Solomon
  59. Progress of Theoretical Physics Supplement No.80 (1984) pp. 76-93 :
    A Field Theoretic Formalism for Electron-Phonon Interactions in Disordered Materials
    Morrel H. Cohen, E. N. Economou and Costas M. Soukoulis
  60. Progress of Theoretical Physics Supplement No.80 (1984) pp. 94-102 :
    Cooper Pairing in the Presence of Inhomogeneous Magnetism
    E. W. Fenton
  61. Progress of Theoretical Physics Supplement No.91 (1987) pp. 284-298 :
    Pion and σ-Meson at Finite Temperature
    Tetsuo Hatsuda and Teiji Kunihiro
  62. Progress of Theoretical Physics Supplement No.121 (1995) pp. 1-428 :
    Novel Use of Legendre Transformation in Field Theory and Many Particle Systems
    Reijiro Fukuda, Masahiro Komachiya, Satoshi Yokojima, Yoko Suzuki, Ko Okumura and Takeshi Inagaki
  63. Progress of Theoretical Physics Supplement No.182 (2009) pp. 1-208 :
    Stationary Phase and Macrovariable
    Reijiro Fukuda

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.