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Hokkaido University Preprint Series in Mathematics >
Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model
| Title: | Spectral Properties of a Dirac Operator in the Chiral Quark Soliton Model |
| Authors: | Arai, Asao Browse this author | | Hayashi, Kunimitsu Browse this author | | Sasaki, Itaru Browse this author |
| Keywords: | Dirac operator | | chiral quark soliton model | | supersymmetry | | spectrum | | ground state |
| Issue Date: | 16-Dec-2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 678 |
| Start Page: | 1 |
| End Page: | 15 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69483 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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