Department of Mathematics,

Hokkaido University

Sapporo,

060-0810, JAPAN

E-mail: arai@math.sci.hokudai.ac.jp

**Spectral analysis of the chiral quark soliton model**

**Abstract:**

We present mathematically rigorous analysis of a Dirac operator $H$
describing the Hamiltonian of the chiral quark soliton model in nuclear
physics. The following aspects are investigated:

(i) a supersymmetric structure of the model;

(ii) the identification of the essential spectrum
of $H$;

(iii) an upper bound for the number of discrete
eignevalues of $H$;

(iv) existence of discrete positive or negative
ground states of $H$;

(v) symmetry reduction of $H$.