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Topologically non--trivial chiral transformations and their representations in a finite model space

R. Alkofer·H. Reinhardt·J. Schlienz·H. Weigel
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Abstract

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The role of this transformation in the presence of a topologically non--trivial chiral field is illuminated. The fermion determinant for such a field configuration is evaluated by summing the discretized eigenvalues of the Dirac Hamiltonian. This discretization is accomplished by demanding certain boundary conditions on the quark fields leaving a finite model space. The properties of two sets of boundary conditions are compared. When the topologically non-trivial chiral transformation is applied to the meson fields the associated transformation of the boundary conditions is shown to be indispensable. A constructive procedure for transforming the boundary conditions is developed.

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R. Alkofer, H. Reinhardt, J. Schlienz, H. Weigel. 1994-04-06. Topologically non--trivial chiral transformations and their representations in a finite model space. https://arxiv.org/abs/hep-ph/9404222

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