open access

https://doi.org/10.14943/83829

https://hdl.handle.net/2115/69483

Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model

英語

ground state

2004-12-16

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

678

1-15

We consider a Dirac operator H acting in the Hilbert space L2(IR3;C4) ○C2, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued function formed out of a function F : IR3 ! IR, called a pro le function, and a vector eld n on IR3, which xes pointwise a direction in the iso-spin space of the pion. We rst 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 IR. We then identify the essential spectrum of H under some condition for F. For a class of pro le 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.

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