Free Energy of Gravitating Fermions

Thirring, Walter

Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 14 (1972), p. 1-26 / Harvested from Numdam

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Publié le : 1972-01-01

@article{RCP25_1972__14__A3_0,
     author = {Thirring, Walter},
     title = {Free Energy of Gravitating Fermions},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     volume = {14},
     year = {1972},
     pages = {1-26},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RCP25_1972__14__A3_0}
}

Thirring, Walter. Free Energy of Gravitating Fermions. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 14 (1972) pp. 1-26. http://gdmltest.u-ga.fr/item/RCP25_1972__14__A3_0/

Bibliographie

1) F.J. Dyson in Statistical Physics, Phase transitions and Superfluidity, 1966 Brandeis University Suramer School in Theoretical Physics, lecture notes ;

F.J. Dyson and A. Lenard, J.Math.Phys. 8 (1967) 423 | MR 2408896 | Zbl 0948.81665

2) J.L. Lebowitz and E. H. Lieb, Phys. Rev. Letter 22. (1969) 631

3) J.-M. Lévy-Leblond, J.Math.Phys. 10 (1969) 806.

4) W. Thirring, Z. Phys. 235 (1970) 339;

P. Hertel and W. Thirring, Annals of Physics 63 (1971).

5) P. Hertel and W. Thirring, CEEN preprint TH. 1338 (1971). | MR 1552579

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 $N = 1$ , $β = 60 ℏ^{2} κ^{- 2} m_{N}^{- 5}$ , $R = 29 ℏ^{2} κ^{- 1} m_{N}^{- 1}$ 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 $λ \to \infty$ . For $N = 1057$ , $β = {(5 M e V)}^{- 1}$ and $R = 100$ km we would have reached the same accuracy for $λ = 1$ .

7) T. Kato, Perturbation theory for linear operators, Berlin, Springer 1966. There the infinite volume case is studied, however, the result also holds for finite volume. | Zbl 0836.47009

8) H.D. Maison, Analyticity of the partition function for finite quantum Systems, CERN preprint TH. 1299 (1971). | MR 303887 | Zbl 0218.47017

9) J. Dieudonné, Eléments d'analyse, Tome I, Paris, Gauthier-Villars 1969. | Zbl 0326.22001

10) B. Simon, J.Math.Phys. 10 (1969) 1123. Again this estimate for infinité volume is a fortiori also valid for finite volume. | MR 246593

11) D. Ruelle, Statistical mechanics - rigorous results, New York, Benjamin 1961. | MR 289084 | Zbl 0177.57301

12) N.N. Bogoliubov Jr., Physica 32 (1966) 933. | MR 207351

13) J. Ginibre, Commun.Math.Phys. 8 (1968) 26. | MR 225552 | Zbl 0155.32701