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**1 - 4**of**4**### Involution Of First Order Differential On Lattice And Continuum Limit

, 2001

"... We prove that differentials of lattice coordinate functions x µ must be algebraically independent of their involutive conjugate, else no correct continuum limit exists. ..."

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We prove that differentials of lattice coordinate functions x µ must be algebraically independent of their involutive conjugate, else no correct continuum limit exists.

### A New Solution to Ginsparg-Wilson Relation from Generalized Staggered Fermion

, 2001

"... A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this antihermitian operator is modified to be “γ 5-hermitian”, it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis ..."

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A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this antihermitian operator is modified to be “γ 5-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. Keywords: staggered fermion, Dirac operator, Ginsparg-Wilson relation, chirality, noncommutative geometry

### A No-Go Theorem For The Compatibility Between Involution Of First Order Differential on Lattice And Continuum Limit

, 2001

"... We prove that differentials of lattice coordinate functions x µ must be algebraic independent to their involutive conjugate, else no correct continuum limit exists. ..."

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We prove that differentials of lattice coordinate functions x µ must be algebraic independent to their involutive conjugate, else no correct continuum limit exists.

### Geometric Origin of Staggered Fermion: Direct Product K-Cycle

, 2001

"... Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. The correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated abelian group where lattice appears as a special case is proved. ..."

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Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. The correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated abelian group where lattice appears as a special case is proved.