Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

402-0878-00L  Field Theory with Symmetries and the Batalin-Vilkovisky Formalism

SemesterAutumn Semester 2019
LecturersM. Schiavina
Periodicitynon-recurring course
Language of instructionEnglish


AbstractThe course is an introduction to the Batalin-Vilkovisky formalism, which provides a rigorous toolkit to treat classical and quantum field theories with symmetries, generalising the BRST approach. The course will feature applications to gauge theories and general relativity, and possibly to theories with defects (boundaries and corners).
ObjectiveThe objective of this course is to expose master and graduate physics students to modern techniques in theoretical and mathematical physics to handle gauge symmetries in classical and quantum field theory. We aim to provide a solid mathematical background for third-semester master and graduate students to adventure further in this research direction.
ContentThe course will start with a review of the BRST formalism expanding on its introduction in Quantum Field Theory II. It will provide a mathematical background on (Lie algebra) cohomology and the necessary requirements to describe the BV formalism, including an introduction to symplectic geometry on graded vector spaces. Applications of the BV formalism to different examples like gauge theories, general relativity and sigma models will be presented, and a discussion on quantisation of classical field theories in this setting, together with possible inclusion of defects, will be considered as concluding topics for the course.