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arXiv · 0907.4137

Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra

Alessandro D'Adda·Noboru Kawamoto·Jun Saito
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Abstract

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.

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Alessandro D'Adda, Noboru Kawamoto, Jun Saito. 2009-07-23. Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra. https://doi.org/10.1103/physrevd.81.065001

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