Minimal doubling fermions and hermiticity

作者：Kamata Syo^*; Tanaka Hidekazu

来源：Progress of Theoretical and Experimental Physics, 2013, (2): 023B05.

DOI：10.1093/ptep/pts093

We analyze the lattice fermion kinetic term using PT symmetry, R-hermiticity, and gamma(5)-hermiticity. R-hermiticity is a condition for Hermite action and it is related to gamma(5)-hermiticity and PT symmetry. Assuming that a translation-invariant kinetic term with continuum and periodic function does not have PT symmetry, it can have R-hermiticity or gamma(5)-hermiticity. We prove that a kinetic term with continuum and periodic function that is PT symmetric does not reduce doublers. As a simple example, we analyze the two-dimensional two-flavor Gross-Neveu model with minimal doubling fermions. The minimal doubling fermions break PT symmetry and R-hermiticity, hence complex or non-Hermite coupling constants are caused by quantum correction.

• 出版日期2013-2