Symmetries of Ginsparg-Wilson Chiral Fermions
arXiv:0901.0572 · doi:10.1103/PhysRevD.80.085023
Abstract
The group structure of the variant chiral symmetry discovered by Luscher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter invariant subgroup, and the factor group, whose elements are its cosets, is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, non-commuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example, free overlap fermions, these non-canonical elements of lattice chiral symmetry are related to complex energy singularities that violate reflection positivity and impede continuation to Minkowski space.
arXiv comment36 pages; PDF only; References added
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Cited by in corpus (6)
- A renormalisation group derivation of the overlap formulation
- A Ginsparg-Wilson approach to lattice CP symmetry, Weyl and Majoranna fermions, and the Higgs mechanism
- A further extension to the group of Ginsparg-Wilson (overlap) chiral symmetries
- A Ginsparg-Wilson approach to lattice symmetry
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