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We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes.
A process-theoretic church of the larger hilbert space
Stefano Gogioso · 1905
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On infinite direct products
John von Neumann · 1939
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An algebraic approach to quantum field theory
Rudolf Haag and Daniel Kastler · 1964
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Theory of Self-Reproducing Automata
John von Neumann · 1966
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On the structure of causal spaces
Erwin H. Kronheimer and Roger Penrose · 1967
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A new topology for curved space-time which incorporates the causal, differential, and conformal structures
Stephen W Hawking, A Ro King, and PJ McCarthy · 1976
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The class of continuous timelike curves determines the topology of spacetime
David B. Malament · 1977
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Simulating physics with quantum computers
Richard P. Feynmann · 1982
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Space-time as a causal set
Luca Bombelli, Joohan Lee, David Meyer, and Rafael D Sorkin · 1987
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Topological quantum field theory
Michael F Atiyah · 1988
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Topological quantum field theory
Edward Witten · 1988
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Frobenius algebras and 2D topological quantum field theories
Joachim Kock · 2003
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Causal sets: Overview and status
Luca Bombelli · 2006
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Algebraic quantum field theory
Hans Halvorson and Michael Müger · 2006
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‘What is a Thing?’: Topos Theory in the Foundations of Physics
Andreas Doering and Chris Isham · 2008
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A topos for algebraic quantum theory
Chris Heunen, Nicolaas P Landsman, and Bas Spitters · 2009
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Terminality implies no-signalling… and much more than that
Bob Coecke · 2016
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Quantum cellular automata and free quantum field theory
Giacomo Mauro D’Ariano and Paolo Perinotti · 2016
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Picturing quantum processes
Bob Coecke and Aleks Kissinger · 2017
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A categorical semantics for causal structure
Aleks Kissinger and Sander Uijlen · 2017
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Towards quantum field theory in categorical quantum mechanics
Stefano Gogioso and Fabrizio Genovese · 2018
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Categorical probabilistic theories
Stefano Gogioso and Carlo Maria Scandolo · 2018
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On the classification of topological field theories
Jacob Lurie et al · 2009
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Domain theory and general relativity
Keye Martin and Prakash Panangaden · 2010
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Spacetime geometry from causal structure and a measurement
Keye Martin and Prakash Panangaden · 2012
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Causal categories: relativistically interacting processes
Bob Coecke and Raymond Lal · 2013
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An overview of quantum cellular automata
Pablo Arrighi · 2019
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Quantum field theory in categorical quantum mechanics
Stefano Gogioso and Fabrizio Genovese · 2019
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Categorical semantics for time travel
Nicola Pinzani, Stefano Gogioso, and Bob Coecke · 2019
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