The BV Laplacian Δ, first introduced by Batalin and Vilkovisky, is a second-order differential operator that appears in the quantum master equation for quantizing gauge theories. The geometric framework for the BV formalism was later recognized by Schwarz as the setting of odd symplectic geometry and Khudaverdian showed that Δ acts covariantly on half-densities on odd symplectic supermanifolds. Building on Ševera’s construction of Δ using a spectral sequence for the de Rham bicomplex (dR , ? + ?), we provide a new, more explicit construction of Δ using the homological perturbation lemma. The fact that Δ is globally well-defined on half-densities is established using Čech complexes. We show moreover that our methods apply in the setting of integral forms, giving a construction naturally integrable over purely odd Lagrangians.

Creator

• Kumar, Nilay

DOI

• https://doi.org/10.21985/n2-g0pq-6y94

Subject

• Mathematics
• Physics

Language

• en

Alternate Identifier

• etdadmin_upload_845582
• http://dissertations.umi.com/northwestern:15776

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright