Geodesic
On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we formulate our results on the essential spectrum of many-particle pseudorelativistic Hamiltonians without magnetic and external potential fields in the spaces of functions, having arbitrary type $\alpha$ of the permutational symmetry. We discover location of the essential spectrum for all $\alpha$ and for some cases we establish new properties of the lower bound of this spectrum, which are useful for study of the discrete spectrum.
Keywords: pseudorelativistic Hamiltonian; many-particle system; permutational symmetry; essential spectrum. 
@article{SIGMA_2006_2_a23,
     author = {Grigorii Zhislin},
     title = {On the {Essential} {Spectrum} of {Many-Particle} {Pseudorelativistic} {Hamiltonians} with {Permutational} {Symmetry} {Account}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2006},
     volume = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a23/}
}
TY  - JOUR
AU  - Grigorii Zhislin
TI  - On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2006
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a23/
LA  - en
ID  - SIGMA_2006_2_a23
ER  - 
%0 Journal Article
%A Grigorii Zhislin
%T On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account
%J Symmetry, integrability and geometry: methods and applications
%D 2006
%V 2
%U http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a23/
%G en
%F SIGMA_2006_2_a23
Grigorii Zhislin. On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a23/

[1] Damak M., “On the spectral theory of dispersive $N$-body Hamiltonians”, J. Math. Phys., 40 (1999), 35–48 | DOI | MR | Zbl

[2] Lewis R. T., Siedentop H., Vugalter S., “The essential spectrum of relativistic multi-particle operators”, Ann. Inst. H. Poincaré Phys. Théor., 67 (1997), 1–28 | MR | Zbl

[3] Lieb E., Yau H.-T., “The stability and instability of relativistic matter”, Comm. Math. Phys., 118 (1988), 177–213 | DOI | MR | Zbl

[4] Reed M., Simon B., Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York–San Francisco–London, 1978 | MR | Zbl

[5] Sigalov A. G., Sigal I. M., “Invariant description, with respect to transpositions of identical particles, of the energy operator spectrum of quantum-mechanical systems”, Teoret. Mat. Fiz., 5:1 (1970), 73–93 (in Russian) | MR

[6] Wigner E. P., Group theory and its application to quantum mechanics, New York, 1959

[7] Math. USSR-Izvestia, 3:3 (1969), 559–616 | DOI | MR | Zbl | Zbl