Free Energy of Gravitating Fermions

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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
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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 $(\lambda N,{\lambda }^{-4/3}\beta ,{\lambda }^{-1/3}R)$ with $N=1$, $\beta =60{\hslash }^2{\kappa }^{-2}{m}_N^{-5}$, $R=29{\hslash }^2{\kappa }^{-1}{m}_N^{-1}$ and $\lambda ={10}^{57}$. Since $N$, $S$ and $R$ are of order unity (if measured in their natural units) and since $\lambda ={10}^{57}$ is sufficiently large, we will describe the above “neutron star” by the limit $\lambda \to \infty$. For $N=1057$, $\beta ={\left(5MeV\right)}^{-1}$ and $R=100$ km we would have reached the same accuracy for $\lambda =1$. 
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
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