López Arcos, Cristhiam ManuelAlzate Lugo, Tomas2025-07-152025-07-152025https://repository.eia.edu.co/handle/11190/7134129 páginasABSTRACT: In this monograph, we review the mathematical foundations of the Batalin-Vilkovisky formalism for treating gauge systems, in the context of homological algebra and graded differential geometry. This formalism leads to an L∞-algebra that encodes all the information of a classical field theory: gauge symmetries, field content, equations of motion, and Noether identities. As illustrative examples, we present the Yang–Mills and Chern–Simons theoriesapplication/pdfspaDerechos Reservados - Universidad EIA, 2025Trabajo de grado - PregradoAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)info:eu-repo/semantics/openAccessBV formalismHomological AlgebraGraded GeometryGauge Theoryhttp://purl.org/coar/access_right/c_abf2