Geodesic
Stability of $n$-particle pseudorelativistic systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 528-537 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a system $Z_n$ of $n$ identical pseudorelativistic particles, we show that under some restrictions on the pair interaction potentials, there is an infinite sequence of numbers $n_s$, $s=1,2,\dots$, such that the system $Z_n$ is stable for $n=n_s$, and the inequality $\sup_sn_{s+1}n_s^{-1}<+\infty$ holds. Furthermore, we show that if the system $Z_n$ is stable, then the discrete spectrum of the energy operator for the relative motion of the system $Z_n$ is nonempty for some values of the total momentum of the particles in the system. The stability of $n$-particle systems was previously studied only for nonrelativistic particles.
Keywords: pseudorelativistic operator, many-particle system, stability, discrete spectrum. 
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     author = {G. M. Zhislin},
     title = {Stability of $n$-particle pseudorelativistic systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {528--537},
     year = {2007},
     volume = {152},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a9/}
}
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G. M. Zhislin. Stability of $n$-particle pseudorelativistic systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 528-537. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a9/

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