
SIGMA 2 (2006), 024, 9 pages mathph/0602050
https://doi.org/10.3842/SIGMA.2006.024
On the Essential Spectrum of ManyParticle Pseudorelativistic Hamiltonians with Permutational Symmetry Account
Grigorii Zhislin
Radiophysical Research Institute, 25/14 Bol'shaya Pechorskaya Str., Nizhny Novgorod, 603950 Russia
Received October 27, 2005, in final form February 07, 2006; Published online February 20, 2006
Abstract
In this paper we formulate our results on the essential spectrum
of manyparticle pseudorelativistic Hamiltonians without
magnetic and external potential fields in the spaces of functions, having arbitrary type α of the permutational
symmetry. We discover location of the essential spectrum for all
α and for some cases we establish new properties of the
lower bound of this spectrum, which are useful for study of the
discrete spectrum.
Key words:
pseudorelativistic Hamiltonian; manyparticle system; permutational symmetry; essential spectrum.
pdf (205 kb)
ps (165 kb)
tex (11 kb)
References
 Damak M., On the spectral theory of dispersive Nbody
Hamiltonians, J. Math. Phys., 1999, V.40, 3548.
 Lewis R.T., Siedentop H., Vugalter S., The essential
spectrum of relativistic multiparticle operators, Ann.
Inst. H. Poincaré Phys. Théor., 1997, V.67, 128.
 Lieb E., Yau H.T., The stability and instability of
relativistic matter, Comm. Math. Phys., 1988, V.118,
177213.
 Reed M., Simon B., Methods of modern mathematical physics. IV
Analysis of operators, New York  San Francisco  London,
Academic Press, 1978.
 Sigalov A.G., Sigal I.M., Invariant description, with respect to
transpositions of identical particles, of the energy operator
spectrum of quantummechanical systems, Teoret. Mat. Fiz.,
1970, V.5, 7393 (in Russian).
 Wigner E.P., Group theory and its application to quantum
mechanics, New York, 1959.
 Zhislin G., Spectrum of differential operators of quantum
mechanical manyparticle system in the spaces of functions of the
given symmetry, Izvest. Akad. Nauk SSSR, Ser. Mat., 1969,
V.33, 590649 (English transl.: Math. USSRIzvestia, 1969,
V.3, 559616).

