Angelos Anastopoulos | Searcharxiv

arXiv2024

Gluing algebraic quantum field theories on manifolds

It has been observed that, given an algebraic quantum field theory (AQFT) on a manifold $M$ and an open cover $\{M_α\}$ of $M$, it is typically not possible to recover the global algebra of observables on $M$ by simply gluing the underlying local algebras subordinate to $\{M_α\}$. Instead of gluing local algebras, we introduce a gluing construction for AQFTs subordinate to $\{M_α\}$ and we show that for simple examples of AQFTs, constructed out of geometric data, gluing the local AQFTs subordinate to $\{M_α\}$ recovers the global AQFT on $M$.

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arXiv2022

Homotopy theory of net representations

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.

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