A New Solution to Ginsparg-Wilson Relation from Generalized Staggered Fermion
Jian Dai, Xing-Chang Song (Theoretical Group, Department of Physics,, Peking University)
TL;DR
This paper introduces a novel anti-hermitian staggered Dirac operator that, when modified to be gamma5-hermitian, offers a new algebraic solution to the Ginsparg-Wilson relation, connecting to noncommutative geometry.
Contribution
It formulates a generalized staggered Dirac operator and modifies it to solve the Ginsparg-Wilson relation using algebraic analysis and redefined chirality.
Findings
Proposes a new anti-hermitian staggered Dirac operator.
Establishes a connection with noncommutative geometry.
Provides a novel algebraic solution to Ginsparg-Wilson relation.
Abstract
A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this anti-hermitian operator is modified to be ``-hermitian'', it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis of Neuberger's overlap construction and a redefinition of chirality.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Noncommutative and Quantum Gravity Theories · Advanced Topics in Algebra