Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-23
Phys.Rev.D81:065001,2010
Physics
High Energy Physics
High Energy Physics - Theory
45 pages
Scientific paper
10.1103/PhysRevD.81.065001
The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required.
D'Adda Alessandro
Kawamoto Noboru
Saito Jun
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