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Authors
Werner Kerler
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Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujikawa includes many more general ones. The index turns out to depend solely on a basic unitary operator. We use spectral representations to analyze the new class and to obtain detailed properties. We also show that our weaker conditions still lead properly to Weyl fermions and to chiral gauge theories.
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We only require generalized chiral symmetry and $gamma_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general construction of them. A basic unitary operator is seen to play a central r^ole in this context. We discuss a number of special cases of the operators and elaborate on various aspects of index relations. We also show that our weaker conditions lead still properly to Weyl fermions and to chiral gauge theories.
Instead of the Ginsparg-Wilson relation only generalized chiral symmetry is required. The resulting much larger class of Dirac operators for massless fermions is investigated and a general construction for them is given. It is also shown that the new class still leads properly to Weyl fermions and to chiral gauge theories.
We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators, we study the basis representations of the chiral projections. We then investigate correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and their consequences, and getting the precise behaviors under gauge transformations and CP transformations. Various further developments include considerations of the explicit form of the effective action and of a representation of the general correlation functions in terms of alternating multilinear forms. For comparison we also consider gauge-field variations and their respective applications. Finally we compare with continuum perturbation theory.
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. The exact flavored chiral symmetry of the staggered fermion gets converted into an unflavored Ginsparg-Wilson chiral symmetry of the new overlap fermion, which also has pairs of exact chiral zero-modes satisfying the Index Theorem. Stability under radiative corrections is checked. A domain wall formulation giving a truncation of this overlap construction is also outlined.
The construction of baryonic operators for determining the N* excitation spectrum is discussed. The operators are designed with one eye towards maximizing overlaps with the low-lying states of interest, and the other eye towards minimizing the number of sources needed in computing the required quark propagators. Issues related to spin identification are outlined. Although we focus on tri-quark baryon operators, the construction method is applicable to both mesons and penta-quark operators.
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