PIRSA:21040027

Lie Algebroids and BRST

APA

Ciambelli, L. (2021). Lie Algebroids and BRST. Perimeter Institute. https://pirsa.org/21040027

MLA

Ciambelli, Luca. Lie Algebroids and BRST. Perimeter Institute, Apr. 20, 2021, https://pirsa.org/21040027

BibTex

          @misc{ pirsa_21040027,
            doi = {10.48660/21040027},
            url = {https://pirsa.org/21040027},
            author = {Ciambelli, Luca},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Lie Algebroids and BRST},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {apr},
            note = {PIRSA:21040027 see, \url{https://pirsa.org}}
          }
          

Abstract

I will give an introduction to the geometric aspects of Lie algebroids and show how they give the correct framework to discuss gauge theories. The analysis is solely based on geometry, and thus applies to every gauge theory, independently of their specific features and dynamics. By thoroughly re-formulating the physical content of gauge theories on Atiyah Lie algebroids, we will show that the BRST construction is part of the formalism, indicating a fascinating interplay between classical geometry and quantum physics. Time permitting, we will show how our setup encompasses gravitational theories too, once the frame bundle and solder form are added to the picture.