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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, Asao1 Browse this author →KAKEN DB | Hayashi, Kunimitsu Browse this author | Sasaki, Itaru Browse this author |
Authors(alt): | 新井, 朝雄1 |
Issue Date: | May-2005 |
Publisher: | American Institute of Physics |
Journal Title: | JOURNAL OF MATHEMATICAL PHYSICS |
Volume: | 46 |
Start Page: | 052306 |
Publisher DOI: | 10.1063/1.1896388 |
Abstract: | We consider a Dirac operator H acting in the Hilbert space L2(R3;C4)(x)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:R3→R, called a profile function, and a vector field n on R3, 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 spectra of H are symmetric with respect to the origin of R. 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. |
Rights: | Copyright © 2005 American Institute of Physics |
Relation: | http://www.aip.org/ |
Type: | article |
URI: | http://hdl.handle.net/2115/5908 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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