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

Journal Article · Sun May 01 00:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1896388· OSTI ID:20699175

Arai, Asao; Hayashi, Kunimitsu; Sasaki, Itaru ^[1]

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1. Department of Mathematics, Hokkaido University, Sapporo 060-0810 (Japan)

We consider a Dirac operator H acting in the Hilbert space L{sup 2}(R{sup 3};C{sup 4})xC{sup 2}, 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:R{sup 3}{yields}R, called a profile function, and a vector field n on R{sup 3}, 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.

• OSTI ID: 20699175
• Journal Information: Journal of Mathematical Physics, Vol. 46, Issue 5; Other Information: DOI: 10.1063/1.1896388; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CHIRAL SYMMETRY
CHIRALITY
DEFORMATION
DIRAC EQUATION
DIRAC OPERATORS
EIGENVALUES
FUNCTIONAL ANALYSIS
GROUND STATES
HAMILTONIANS
HILBERT SPACE
ISOSPIN
NUCLEAR PHYSICS
PIONS
QUARK MODEL
QUARKS
SOLITONS
SUPERSYMMETRY
TRANSFORMATIONS
VECTOR FIELDS