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- Title
Homotopy theory of net representations.
- Authors
Anastopoulos, Angelos; Benini, Marco
- Abstract
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net Quillen adjunction between the model categories of net representations, which is furthermore, a Quillen equivalence when the morphism is a weak equivalence. These techniques are applied in the context of homotopy algebraic quantum field theory with values in cochain complexes. In particular, an explicit construction is presented that produces constant net representations for Maxwell p -forms on a fixed oriented and time-oriented globally hyperbolic Lorentzian manifold.
- Subjects
ALGEBRAIC field theory; HOMOTOPY theory; REPRESENTATION theory; QUANTUM field theory; ALGEBRA
- Publication
Reviews in Mathematical Physics, 2023, Vol 35, Issue 5, p1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X23500083