Quantum $L_\infty$ Algebras and the Homological Perturbation Lemma

Autor:	Doubek, Martin, Jurčo, Branislav, Pulmann, Ján
Rok vydání:	2017
Předmět:	Mathematical Physics Mathematics - Algebraic Topology Mathematics - Quantum Algebra
Zdroj:	Comm. Math. Phys. 367 (2019) 215-240
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-019-03375-x
Popis:	Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ 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 $L_\infty$ algebra. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1712.02696 Zobrazit plný text záznamu View this record from Arxiv