scholarly journals Functorial Evolution of Quantum Fields

2021 ◽  
Vol 9 ◽  
Author(s):  
Stefano Gogioso ◽  
Maria E. Stasinou ◽  
Bob Coecke
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cellular Automata ◽  
Quantum Field ◽  
Quantum Fields ◽  
Causal Order ◽  
Algebraic Quantum ◽  
Starting Point ◽  
Algebraic Framework ◽  
Definition Of

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.

scholarly journals Quantum Fields as Category Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1727
Author(s):  
Hayato Saigo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Quantum Fields ◽  
New Approach ◽  
Algebraic Quantum ◽  
Topological Quantum ◽  
Probabilistic Structure ◽  
Conceptual Relationships ◽  
Category Algebras

In the present paper, we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also be discussed.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals Algebraic Quantum Field Theory on Spacetimes with Timelike Boundary

2018 ◽  
Vol 19 (8) ◽  
pp. 2401-2433 ◽  
Author(s):  
Marco Benini ◽  
Claudio Dappiaggi ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum
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