Song Xing-Chang

On the gauge invariance and anomaly-free condition of the Wess-Zumino-Witten effective action

A global anomaly-free condition and a non-abelian gauge invariant Wess-Zumino-Witten effective action with less terms have been found by a systematical method rather than by trial and error. The condition requires the difference between the left- and right-handed Chern-Simon five-forms wrt the gauge group must vanish and it turns out to be the usual condition in the local sense.

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

Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. We prove the correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated Abelian groups where a lattice appears as a special case.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.

Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations

Canonical differential calculus is defined for finitely generated abelian group with an involution existing consistently. Two such canonical calculi are found out. Fermionic representation for canonical calculus is defined based on quantized calculus. Fermionic representations for above-mentioned two canonical calculi are searched.Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.

QUANTUM DYNAMICAL R-MATRIX FROM FUSION

A quantum dynamical R-matrix (QDRM) with three distinct eigenvalues, which is a trigonometric solution of the Gervais–Neven–Felder equation, is constructed from the fusion of the simplest 4 × 4 trigonometric QDRM of Hecke type for sl(2).

Irreducible Representations of Quantum sl(3) Enveloping Algebra

By referring to the construction method of finding representations of classical group, we developed a parallel method with which one can construct irreducible representations of quantum sl(3) enveloping algebra explicitly.

The Hn Sigma-Models and Self-Dual SU(n) Yang-Mills Fields In Four-Dimensional Euclidean Space

The Hn σ-models, i.e., non-linear σ-models taking-values on the symmetric coset space SL(n,c)/SU(n), both in two-dimensional and four-dimensional Euclidean space, are formulated. The relations with self-duel SU(n) Yang-Mills fields are also discussed.

A no-go theorem for compatibility between involutions of first order differentials on a lattice and continuum limit

We prove that the following three properties cannot match each other on a lattice, that differentials of coordinate functions are algebraically dependent on their involutive conjugates, that the involution on a lattice is an antihomomorphism, and that differential calculus has a natural continuum limit.

Dirac Neutrino Masses in NCG

Several models in NCG with mild changes to the standard model(SM)are introduced to discuss the neutrino mass problem. We use two constraints, Poincar

Supercoherent State of the Orthosymplectic (2,1) Superalgebra

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The Reduction of Differential Calculus on Direct Product Group

duality and gauge anomaly free, to discuss the possibility of containing right-handed neutrinos in them. Our work shows that no model in this paper, with each generation containing a right-handed neutrino, can satisfy these two constraints in the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.Several models in noncommutative geometry (NCG) with mild changes to the standard model are introduced to discuss the neutrino mass problem. We use two constraints, Poincare duality and gauge anomaly free, to discuss the possibility of containing right-handed neutrinos in them. Our work shows that no model in this paper, with each generation containing a right-handed neutrino, can satisfy these two constraints at the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.