Comments on chiral invariant and non-hermitian lattice fermion actions

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Abstract Discussions are made on the structure of chiral-invariant and non-hermitian actions of lattice fermions. With the help of the Ward-Takahashi identity a general conclusion can be derived that there must be species doublers in any chiral invariant models provided that the model is well-regularized, that is, there is no singularity in the propagator after introducing a fermion mass on the lattice. A better model has been found in two dimensions in the sense that the number of species doublers is smaller than that of the naive Dirac action.

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