2019-10-22T03:50:56Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694832018-04-25T23:44:09Zhdl_2115_45007hdl_2115_116Spectral Properties of a Dirac Operator in the Chiral Quark Soliton ModelArai, AsaoHayashi, KunimitsuSasaki, Itaruopen accessDirac operatorchiral quark soliton modelsupersymmetryspectrumground state410We 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.2004-12-16engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83829http://hdl.handle.net/2115/6948310.14943/83829Hokkaido University Preprint Series in Mathematics678115https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69483/1/pre678.pdfapplication/pdf111.55 KB2004-12-16