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Spectral properties of a Dirac operator in the chiral quark soliton model

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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
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
Type: article
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)

Submitter: 新井 朝雄

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