Quantum $L_\infty$ Algebras and the Homological Perturbation Lemma
Mathematical Physics
2023-07-31 v3 Algebraic Topology
math.MP
Quantum Algebra
Abstract
Quantum algebras are a generalization of algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum algebra via the homological perturbation lemma and show that it's given by a Feynman diagram expansion, computing the effective action in the finite-dimensional Batalin-Vilkovisky formalism. We also construct a homotopy between the original and this effective quantum algebra.
Keywords
Cite
@article{arxiv.1712.02696,
title = {Quantum $L_\infty$ Algebras and the Homological Perturbation Lemma},
author = {Martin Doubek and Branislav Jurčo and Ján Pulmann},
journal= {arXiv preprint arXiv:1712.02696},
year = {2023}
}
Comments
v2: 27 pages, fixed typos and the section 4.4; v3: published version - shortened and removed the appendix on relationship between quantum master actions and brackets