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This paper is a brief mathematical excursion which starts from quantum electrodynamics and leads to the Moebius function of the Tamari lattice of planar binary trees, within the framework of groups of tree-expanded series. First we recall Brouders expansion of the photon and the electron Greens functions on planar binary trees, before and after the renormalization. Then we recall the structure of Connes and Kreimers Hopf algebra of renormalization in the context of planar binary trees, and of their dual group of tree-expanded series. Finally we show that the Moebius function of the Tamari posets of planar binary trees gives rise to a particular series in this group.
We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to p
Experimental quantum information processing with superconducting circuits is rapidly advancing, driven by innovation in two classes of devices, one involving planar micro-fabricated (2D) resonators, and the other involving machined three-dimensional
In this article, we put forward a new approach to electrodynamics of materials. Based on the identification of induced electromagnetic fields as the microscopic counterparts of polarization and magnetization, we systematically employ the mutual funct
Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields model. Fix $nge 1$ and $beta>0$. We start at time 0 with the tree composed of a root only. At any ti
Tree tensor network descriptions of critical quantum spin chains are empirically known to reproduce correlation functions matching CFT predictions in the continuum limit. It is natural to seek a more complete correspondence, additionally incorporatin