Communications in Mathematical Physics

, Volume 158, Issue 2, pp 373–396 | Cite as

Semiclassical approximation in Batalin-Vilkovisky formalism

  • Albert Schwarz


The geometry of supermanifolds provided with aQ-structure (i.e. with an odd vector fieldQ satisfying {Q, Q}=0), aP-structure (odd symplectic structure) and anS-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.


Neural Network Statistical Physic Complex System Gauge Theory Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Batalin, I., Vilkovisky, G.: Gauge algebra and quantization. Phys. Lett.102B, 27 (1981); Quantization of gauge theories with linearly dependent generators. Phys. Rev.D29, 2567 (1983)Google Scholar
  2. 2.
    Schwarz, A.: Geometry of Batalin-Vilkovisky quantization. Commun. Math. Phys.155, 249 (1993)Google Scholar
  3. 3.
    Witten, E.: A note on the antibracket formalism. Mod. Phys. LettA5, 487 (1990)Google Scholar
  4. 4.
    Schwarz, A.: The partition function of a degenerate functional. Commun. Math. Phys.67, 1 (1979)Google Scholar
  5. 5.
    Witten, E.: TheN matrix model and gaugedWZW models. Preprint IASSNS-HEP-91126Google Scholar
  6. 6.
    Dold, A.: Lectures on algebraic topology. Berlin, Heidelberg, New York: Springer 1972Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Albert Schwarz
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

Personalised recommendations