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

Understand

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.