Free Energy of Gravitating Fermions

Walter Thirring

Recherche Coopérative sur Programme n°25 (1972)

  • Volume: 14, page 1-26

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Thirring, Walter. "Free Energy of Gravitating Fermions." Recherche Coopérative sur Programme n°25 14 (1972): 1-26. <http://eudml.org/doc/274096>.

@article{Thirring1972,
author = {Thirring, Walter},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {1-26},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Free Energy of Gravitating Fermions},
url = {http://eudml.org/doc/274096},
volume = {14},
year = {1972},
}

TY - JOUR
AU - Thirring, Walter
TI - Free Energy of Gravitating Fermions
JO - Recherche Coopérative sur Programme n°25
PY - 1972
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 14
SP - 1
EP - 26
LA - eng
UR - http://eudml.org/doc/274096
ER -

References

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  1. 1) F.J. Dyson in Statistical Physics, Phase transitions and Superfluidity, 1966Brandeis University Suramer School in Theoretical Physics, lecture notes ; 
  2. F.J. Dyson and A. Lenard, J.Math.Phys.8 (1967) 423 Zbl0948.81665MR2408896
  3. 2) J.L. Lebowitz and E. H. Lieb, Phys. Rev. Letter22. (1969) 631 
  4. 3) J.-M. Lévy-Leblond, J.Math.Phys.10 (1969) 806. 
  5. 4) W. Thirring, Z. Phys.235 (1970) 339; 
  6. P. Hertel and W. Thirring, Annals of Physics63 (1971). Zbl0227.47034
  7. 5) P. Hertel and W. Thirring, CEEN preprint TH. 1338 (1971). MR1552579
  8. 6) A typical “neutron star” of 10 57 particles at a temperature of 5 MeV and enclosed into a sphere of 100 km radius corresponds to ( λ N , λ - 4 / 3 β , λ - 1 / 3 R ) with N = 1 , β = 60 2 κ - 2 m N - 5 , R = 29 2 κ - 1 m N - 1 and λ = 10 57 . Since N , S and R are of order unity (if measured in their natural units) and since λ = 10 57 is sufficiently large, we will describe the above “neutron star” by the limit λ . For N = 10 57 , β = ( 5 M e V ) - 1 and R = 100 km we would have reached the same accuracy for λ = 1
  9. 7) T. Kato, Perturbation theory for linear operators, Berlin, Springer1966. There the infinite volume case is studied, however, the result also holds for finite volume. Zbl0836.47009
  10. 8) H.D. Maison, Analyticity of the partition function for finite quantum Systems, CERN preprint TH. 1299 (1971). Zbl0218.47017MR303887
  11. 9) J. Dieudonné, Eléments d'analyse, Tome I, Paris, Gauthier-Villars1969. Zbl0326.22001
  12. 10) B. Simon, J.Math.Phys.10 (1969) 1123. Again this estimate for infinité volume is a fortiori also valid for finite volume. MR246593
  13. 11) D. Ruelle, Statistical mechanics - rigorous results, New York, Benjamin1961. Zbl0177.57301MR289084
  14. 12) N.N. Bogoliubov jr., Physica32 (1966) 933. MR207351
  15. 13) J. Ginibre, Commun.Math.Phys.8 (1968) 26. Zbl0155.32701MR225552

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