Topological foundations of physics
pp. 245-271
in: Shyam Wuppuluri, Francisco A. Doria (eds), The map and the territory, Berlin, Springer, 2018Abstract
Topology and geometry have played an important role in our theoretical understanding of quantum field theories. One of the most interesting applications of topology has been the quantization of certain coupling constants. In this paper, we present a general framework for understanding the quantization itself in the light of group cohomology. This analysis of the cohomological aspects of physics leads to reconsider the very foundations of mechanics in a new light.