Twist Quantization of String and Hopf Algebraic Symmetry

Asakawa, Tsuguhiko; Watamura, Satoshi

doi:10.3842/sigma.2010.068

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Hopf Algebraic Structure Of the Lattice Superalgebra1

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2010

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“…As has been developed in recent years, extending the notion of the symmetry in a field theory to the Hopf algebraic one brings us still useful frameworks in some specific cases especially in noncommutative theories [41,52,53,54,55]. A slightly different applications are found in [16].…”

Section: Hopf Algebraic Structure Of the Lattice Superalgebramentioning

confidence: 99%

Formulation of supersymmetry on a lattice as a representation of a deformed superalgebra

2010

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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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