Skip to main content
SpringerLink
Log in

Path Integral Representation of Quantum Statistical Mechanics

  • Chapter
  • First Online:
Path Integral Quantization and Stochastic Quantization

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 165))

  • 324 Accesses

Abstract

In this chapter, we discuss the path integral representation of quantum statistical mechanics with the following two methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

Chapter 4. Section 4.1

  1. Feynman, R.P. and Hibbs, A.R.; ”Quantum Mechanics and Path Integrals”, McGraw-Hill, 1965, New York, Chapter 10.

    Google Scholar 

  2. Feynman, R.P.; ”Statistical Mechanics”, Benjamin, 1972, Massachusetts.

    Google Scholar 

  3. Kadanoff, L.P. and Baym, G.; ”Quantum Statistical Mechanics”, Benjamin, 1962, Massachusetts.

    Google Scholar 

  4. Parisi, G.; ”statistical Field Theory”, Benjamin Cummings, 1989, Massachusetts, Chapters 13 through 19.

    Google Scholar 

  5. Casher, A., Lurie, D. and Revzen, M.; J. Math. Phys. 9, (1968), 1312.

    Google Scholar 

Chapter 4. Section 4.2

  1. Matsubara, T.; Prog. Theor. Phys. 13, (1955), 628, 631; 14, (1955), 351.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Fetter, A.L. and Walecka, J.D.; ”Quantum Theory of Many-particle Systems”, McGraw-Hill, 1971, New York, Chapter 7.

    Google Scholar 

  3. Fradkin, E.S.; Doklady. Akad. Nauk. SSSR. 125, (1959), 66, 311; JETP. 36, (1959), 952, 1286.

    MathSciNet  Google Scholar 

Chapter 4. Section 4.3

  1. Fradkin, E.S.; Proc. P.N. Lebedev Phys. Institute. Vol. 29. (1965), 1, Chapter 2.

    Google Scholar 

Chapter 4. Section 4.4

  1. Sherrington, D.; J. Phys. C4, (1971), 401.

    ADS  Google Scholar 

  2. Stratonovich, R.L.; Doklady. Akad. Nauk. SSSR. 115, (1957), 1097.

    Google Scholar 

  3. Hubbard, J.; Phys. Rev. Letters. 3, (1959), 77.

    Article  ADS  Google Scholar 

  4. Papadopoulos, G. and Devreese, J.T., ed.; ”Path Integrals and Their Applications in Quantum, Statistical and Solid State Physics”, Plenum Press, 1978, New York.: Lectures by Sherrington, D., Papadopoulos, G., Muhlschlegel, B. and Wiegel, F.W.

    Google Scholar 

  5. Blankenbecler, R., Scalapino, D.J. and Suger, R.L.; Phys. Rev. D24, (1981), 2278.

    Google Scholar 

  6. Frohlich, H.; Advanc. Phys. 3, (1954), 325.

    Article  ADS  Google Scholar 

  7. Feynman, R.P.; Phys. Rev. 97, (1955), 660.

    Article  MATH  ADS  Google Scholar 

  8. Feynman, R.P. and Hibbs, A.R.; ”Quantum Mechanics and Path Integrals”, McGraw-Hill, 1965, New York, Chapter 11, Section 11.4.

    Google Scholar 

  9. Feynman, R.P.; ”Statistical Mechanics”, Benjamin, 1972, Massachusetts, Chapter 8, Sections 8.3 through 8.5.

    Google Scholar 

  10. Donsker, M.D. and Varadhan, S.R.S.; Commun. Pure. Appl. Math. 28, (1975) 1, 279, 29, (1976), 389.

    Article  MATH  MathSciNet  Google Scholar 

  11. Adamovsky, J., Gerlach, B. and Leschke, H.; Phys. Lett. A79, (1980), 249.

    ADS  Google Scholar 

  12. Donsker, M.D. and Varadhan, S.R.S.; Commun. Pure. Appl. Math. 36, (1983), 183, 505.

    Article  MATH  MathSciNet  Google Scholar 

  13. Brosens, F. and Devreese, J.T.; J. Math. Phys. 25, (1984), 1752.

    Article  ADS  MathSciNet  Google Scholar 

  14. Donsker, M.D. and Varadhan, S.R.S.; Commun. Math. Phys. 97, (1985), 187.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Alexandrou, C., Fleischer, W. and Rosenfelder, R.; Phys. Rev. Lett. 65, (1990), 2615.

    Article  ADS  Google Scholar 

  16. Alexandrou, C. and Rosenfelder, R.; Phys. Rep. 215, (1992), 1.

    Google Scholar 

  17. Devreese, J.T. and Brosens, F.; Phys. Rev. B45, (1992), 6459.

    ADS  Google Scholar 

  18. Rosenfelder, R. and Schreiber, A.W.; Phys. Rev. D53, (1996), 3337, 3354.

    ADS  Google Scholar 

Download references

Editor information

Editors and Affiliations

  1. M.H. Company, Ltd, Tokyo, Japan, 1-15-23 Oyamadai, 158-0086 Setagaya-ku, Tokyo, Japan

    Michio Masujima Ph. D.

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2000). Path Integral Representation of Quantum Statistical Mechanics. In: Masujima, M. (eds) Path Integral Quantization and Stochastic Quantization. Springer Tracts in Modern Physics, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48162-1_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-48162-1_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66542-7

  • Online ISBN: 978-3-540-48162-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation