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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83829

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
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

Submitter: 数学紀要登録作業用

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