Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

Jian Qiu; Maxim Zabzine

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 5, page 415-471
  • ISSN: 0044-8753

Abstract

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These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.

How to cite

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Qiu, Jian, and Zabzine, Maxim. "Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications." Archivum Mathematicum 047.5 (2011): 415-471. <http://eudml.org/doc/246633>.

@article{Qiu2011,
abstract = {These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.},
author = {Qiu, Jian, Zabzine, Maxim},
journal = {Archivum Mathematicum},
keywords = {Batalin-Vilkovisky formalism; graded symplectic geometry; graph homology; perturbation theory; Batalin-Vilkovisky formalism; graded symplectic geometry; graph homology; perturbation theory},
language = {eng},
number = {5},
pages = {415-471},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications},
url = {http://eudml.org/doc/246633},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Qiu, Jian
AU - Zabzine, Maxim
TI - Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 5
SP - 415
EP - 471
AB - These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.
LA - eng
KW - Batalin-Vilkovisky formalism; graded symplectic geometry; graph homology; perturbation theory; Batalin-Vilkovisky formalism; graded symplectic geometry; graph homology; perturbation theory
UR - http://eudml.org/doc/246633
ER -

References

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