Notes on derived geometric formulations in physics

Date

2022-6-21

Author

Berktav, Kadri İlker

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This is an overview on certain higher structural constructions in physics. Main motivations of our current attempt are as follows: (i) to provide a brief introduction to the basics of derived algebraic geometry, (ii) to understand how certain derived objects naturally appear in physics and give rise to a formal mathematical treatment, and (iii) to investigate how the notion of a factorization algebra together with certain higher categorical structures come into play to encode the structure of observables in physics. Adopting such a heavy and relatively enriched language allows us to formalize the notions of quantization and observables in quantum field theory as well. This document is organized to explain the underlying mathematical treatment for each task in an expository manner.

Subject Keywords

Derived algebraic geometry, formulations of field theories, factorization algebras and quantization, stacks and moduli spaces, formal moduli problems

URI

https://hdl.handle.net/11511/116215

Collections

Department of Mathematics, Article