Yang-baxterization of the quantum dilogarithm

A new solution of the Yang–Baxter equation with spectral parameter is found. The resulting $R$-matrix $R(x)$ is an operator in $\mathcal H\otimes\mathcal H$, where $\mathcal H=L_2(\mathbb R)$. This $R$-matrix is required to justify the solution of the sine-Gordon model on the discrete space-time. Bibliography: 18 titles.