Quantum L∞ Algebras and the Homological Perturbation Lemma View Full Text


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Article Info

DATE

2019-04

AUTHORS

Martin Doubek, Branislav Jurčo, Ján Pulmann

ABSTRACT

Quantum L∞ algebras are a generalization of L∞ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum L∞ 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∞ algebra. More... »

PAGES

215-240

References to SciGraph publications

  • 2015-11. Homological Perturbation Theory for Nonperturbative Integrals in LETTERS IN MATHEMATICAL PHYSICS
  • 2009-07. Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras in LETTERS IN MATHEMATICAL PHYSICS
  • 2013-06. Solving the Noncommutative Batalin–Vilkovisky Equation in LETTERS IN MATHEMATICAL PHYSICS
  • 2013-08. Quantum Open-Closed Homotopy Algebra and String Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993-07. Geometry of Batalin-Vilkovisky quantization in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1962-12. Introduction in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2004-05. Semidensities on Odd Symplectic Supermanifolds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1987-09. Applications of perturbation theory to iterated fibrations in MANUSCRIPTA MATHEMATICA
  • 2014-09. Homotopy Classification of Bosonic String Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-07. Loop Homotopy Algebras in Closed String Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-019-03375-x

    DOI

    http://dx.doi.org/10.1007/s00220-019-03375-x

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