In this note, we would like to provide a conceptional introduction to the
interaction between derived geometry and physics based on the formalism that
has been heavily studied by Kevin Costello. Main motivations of our current
attempt are as follows: (i) to provide a brief introduction to derived
algebraic geometry, which can be, roughly speaking, thought of as a higher
categorical refinement of an ordinary algebraic geometry, (ii) to understand
how certain derived objects naturally appear in a theory describing a
particular physical phenomenon and give rise to a formal mathematical
treatment, such as redefining a perturbative classical field theory (or its
quantum counterpart) by using the language of derived algebraic geometry, and
(iii) how the notion of factorization algebra together with certain higher
categorical structures come into play to encode the structure of so-called
observables in those theories by employing certain cohomological/homotopical
methods. Adopting such a heavy and relatively enriched language allows us to
formalize the notion of quantization and observables in quantum field theory as
well.Comment: 14 pages. This note serves as an introductory survey on certain
mathematical structures encoding the essence of Costello's approach to
derived-geometric formulation of field theories and the structure of
observables in an expository manne
