Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model
Preprint Series # 678 Arai, Asao and Hayashi, Kunimitsu and Sasaki, Itaru Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model. (2004); AbstractWe consider a Dirac operator $H$ acting
in the Hilbert space $L^2(\BbbR^3;\BbbC^4)\otimes \BbbC^2$,
which describes a Hamiltonian
of the chiral quark soliton model
in nuclear physics. The mass term of $H$ is a matrixvalued
function formed out of a function $F:\BbbR^3 \to \BbbR$,
called a profile function, and a vector field ${\bf n}$
on $\BbbR^3$, which fixes pointwise
a direction in the isospin space of the pion.
We first show that, under suitable conditions,
$H$ may be regarded as a generator of a supersymmetry.
In this case, the spetra of $H$ are symmetric with respect
to the origin of $\BbbR$.
We then identify the essential spectrum of $H$ under some condition
for $F$.
For a class of profile functions $F$, we derive an upper bound
for the number of discrete eigenvalues of $H$. Under suitable
conditions,
we show the existence of a positive energy ground state
or a negative energy ground state
for a family of scaled deformations of $H$.
A symmetry reduction of $H$ is also discussed.
Finally a unitary transformation
of $H$ is given, which may have a physical interpretation.
Item Type:  Preprint 

Uncontrolled Keywords:  Dirac operator, chiral quark soliton model,
supersymmetry, spectrum, ground state


Subjects:  81xx QUANTUM THEORY 

ID Code:  645 

