# Notes on Derived Geometric Formulations in Physics

## TL;DR

This paper provides an overview of advanced geometric and algebraic structures, like derived algebraic geometry and factorization algebras, to formalize concepts of quantization and observables in quantum field theory.

## Contribution

It introduces derived algebraic geometry and higher categorical structures as tools to formalize physical notions of quantization and observables.

## Key findings

- Derived algebraic geometry naturally appears in physics.
- Factorization algebras encode observable structures.
- Formalization of quantization in quantum field theory.

## Abstract

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects naturally appear in physics and give rise to formal mathematical treatment, and (iii) to investigate how factorization algebras 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 examine each task listed above in an expository manner.