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arXiv · 1503.06922

General solution of cyclic Leibniz rule

Daisuke Kadoh·Naoya Ukita
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Abstract

We study the general solution of the cyclic Leibniz rule (CLR) which was recently proposed as a new approach to the lattice supersymmetry. Introducing some mathematical preliminaries related to the cyclic symmetry, we find the general solution of the 2-body CLR for the naive symmetric difference operator. The main theorems of this paper state that the general solution can be uniquely expressed as (A) a linear combination of the two fundamental solutions with cyclic invariant coefficients, and (B) a linear combination of the minimal solutions with complex coefficients. Moreover, an extension to the general difference operators is also discussed.

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Daisuke Kadoh, Naoya Ukita. 2015-03-24. General solution of cyclic Leibniz rule. https://doi.org/10.1093/ptep/ptv140

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