Journal of Operator Theory

Volume 57, Issue 2, Spring 2007 pp. 429-441.

Nonrelativistic limit of the Abstract Chiral Quark Soliton Model and confining effects

Authors: Tadahiro Miyao
Author institution: Zentrum Mathematik, Technische Universitaet, Muenchen, D-85747, Germany

Summary: We consider an abstract version of a Dirac operator which describes a Hamiltonian of the chir al quark soliton model (CQSM) in nuclear physics. The mass term of the Hamiltonian describing the concrete CQSM is a matrix-va lued function. Hence, the abstract CQSM Hamiltonian has structures different from the stand ard Dirac operator. We discuss the nonrelativistic limit of the abstract CQSM Hamiltonian and show that a binding potential appears as an effective potential. As an application of this abstract result, we derive the nonrelativistic limit of the concrete CQSM.

Keywords: We consider an abstract version of a Dirac operator which describes a Hamiltonian of the chir al quark soliton model (CQSM) in nuclear physics. The mass term of the Hamiltonian describing the concrete CQSM is a matrix-va lued function. Hence, the abstract CQSM Hamiltonian has structures different from the stand ard Dirac operator. We discuss the nonrelativistic limit of the abstract CQSM Hamiltonian and show that a binding potential appears as an effective potential. As an application of this abstract result, we derive the nonrelativistic limit of the concrete CQSM.

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