
SIGMA 2 (2006), 018, 12 pages mathph/0602012
https://doi.org/10.3842/SIGMA.2006.018
Mathematical Analysis of a Generalized Chiral Quark Soliton Model
Asao Arai
Department of Mathematics, Hokkaido University, Sapporo, 0600810, Japan
Received October 18, 2005, in final form January 25, 2006; Published online February 03, 2006
Abstract
A generalized version of the socalled chiral quark soliton model (CQSM)
in nuclear physics is introduced. The Hamiltonian of the generalized CQSM
is given by a Dirac type operator with a mass term being an
operatorvalued function. Some mathematically rigorous results on the model are reported.
The subjects included are: (i) supersymmetric structure; (ii)
spectral properties; (iii) symmetry reduction; (iv) a unitarily equivalent model.
Key words:
chiral quark soliton model; Dirac operator; supersymmetry; ground state; symmetry reduction.
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References
 Arai A., Hayashi K., Sasaki I.,
Spectral properties of a Dirac operator in the chiral
quark soliton model, J. Math. Phys., 2005, V.46, N 5, 052360, 12 pages.
 Kalf H., Yamada O.,
Essential selfadjointness of ndimensional Dirac
operators with a variable mass term,
J. Math. Phys., 2001, V.42, 26672676.
 Reed M., Simon B.,
Methods of modern mathematical physics I:
Functional analysis, New York, Academic Press, 1972.
 Reed M., Simon B.,
Methods of modern mathematical physics IV:
Analysis of operators, New York, Academic Press, 1978.
 Sawado N., The SU(3) dibaryons in the
chiral quark soliton model, Phys. Lett. B, 2002, V.524, 289296.
 Sawado N., Private communication.
 Thaller B., The Dirac equation, SpringerVerlag, 1992.

