Functorial evolution of quantum fields

• URL: http://arxiv.org/abs/2003.13271v1
• Date: Mon, 30 Mar 2020 08:39:22 GMT
• Title: Functorial evolution of quantum fields
• Authors: Stefano Gogioso, Maria E. Stasinou and Bob Coecke
• Abstract summary: We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory.

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