There are a few lectures about topological quantum field theory of Graeme Segal on youtube. The first one is this.
I am really interested in the mathematical descriptions of classical mechanics, special relativity, quantum theory,... that he gives in this first lecture.
I do not understand everything he says here. For example, I don't see why he says that an "ontology is a functor", and I don't know what is a $*$-algebra.
Do you know of a book summarizing these mathematical physics topics and explaining what Segal is doing here, written at the level of a mathematics bachelor or a physics graduate student? (It can assume knowledge of Lie groups, topology, some category theory,... but still be explicit - for example explaining why "ontology is a functor")