The embedding structure and the shift operator of the U(1) lattice current algebra

TL;DR

This paper explores the embedding structure and shift operator of the U(1) lattice current algebra, classifying automorphisms and presenting a shift operator with a quantum dilogarithm factorization.

Contribution

It provides a detailed classification of inner realizations of the shift automorphism and introduces a specific shift operator involving quantum dilogarithms.

Findings

Classified inner realizations of the shift automorphism for odd lattice sites

Presented a shift operator with quantum dilogarithm factorization

Connected results to Faddeev and Volkov's work on quantum dilogarithms

Abstract

The structure of block-spin embeddings of the U(1) lattice current algebra is described. For an odd number of lattice sites, the inner realizations of the shift automorphism areclassified. We present a particular inner shift operator which admits a factorization involving quantum dilogarithms analogous to the results of Faddeev and Volkov.