Functorial Evolution of Quantum Fields
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 menti...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2021-07-01
|
| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.534265/full |
| _version_ | 1818440666697433088 |
|---|---|
| author | Stefano Gogioso Maria E. Stasinou Bob Coecke |
| author_facet | Stefano Gogioso Maria E. Stasinou Bob Coecke |
| author_sort | Stefano Gogioso |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T18:15:59Z |
| format | Article |
| id | doaj.art-567c8840d62a45fc8c0d052531a7de98 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-14T18:15:59Z |
| publishDate | 2021-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-567c8840d62a45fc8c0d052531a7de982022-12-21T22:52:11ZengFrontiers Media S.A.Frontiers in Physics2296-424X2021-07-01910.3389/fphy.2021.534265534265Functorial Evolution of Quantum FieldsStefano GogiosoMaria E. StasinouBob CoeckeWe 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.https://www.frontiersin.org/articles/10.3389/fphy.2021.534265/fullcausalityquantum field theoryrelativityalgebraic quantum field theoryquantum cellular automata |
| spellingShingle | Stefano Gogioso Maria E. Stasinou Bob Coecke Functorial Evolution of Quantum Fields Frontiers in Physics causality quantum field theory relativity algebraic quantum field theory quantum cellular automata |
| title | Functorial Evolution of Quantum Fields |
| title_full | Functorial Evolution of Quantum Fields |
| title_fullStr | Functorial Evolution of Quantum Fields |
| title_full_unstemmed | Functorial Evolution of Quantum Fields |
| title_short | Functorial Evolution of Quantum Fields |
| title_sort | functorial evolution of quantum fields |
| topic | causality quantum field theory relativity algebraic quantum field theory quantum cellular automata |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2021.534265/full |
| work_keys_str_mv | AT stefanogogioso functorialevolutionofquantumfields AT mariaestasinou functorialevolutionofquantumfields AT bobcoecke functorialevolutionofquantumfields |