Quantum Field Theory and Coalgebraic Logic in Theoretical Computer\n Science

2016/12/29 by Gianfranco Basti, Basti, Gianfranco, Antonio Capolupo +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Computer and information sciences #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Mathematical Physics (math-ph) #Parallel Computing and Optimization Techniques #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1701.00527

openalex publication_date 2016/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we suggest that in the framework of the Category Theory it is\npossible to demonstrate the mathematical and logical \dual equivalence\nbetween the category of the q-deformed Hopf Coalgebras and the category of\nthe q-deformed Hopf Algebras in QFT, interpreted as a thermal field theory.\nEach pair algebra-coalgebra characterizes, indeed, a QFT system and its\nmirroring thermal bath, respectively, so to model dissipative quantum systems\npersistently in far-from-equilibrium conditions, with an evident significance\nalso for biological sciences. The q-deformed Hopf Coalgebras and the\nq-deformed Hopf Algebras constitute two dual categories because characterized\nby the same functor T, related with the Bogoliubov transform, and by its\ncontravariant application T^op, respectively. The \q-deformation\nparameter, indeed, is related to the Bogoliubov angle, and it is effectively a\nthermal parameter. Therefore, the different values of q identify univocally,\nand then label, the vacua appearing in the foliation process of the quantum\nvacuum. This means that, in the framework of Universal Coalgebra, as general\ntheory of dynamic and computing systems ("labelled state-transition systems"),\nthe so labelled infinitely many quantum vacua can be interpreted as the Final\nCoalgebra of an "Infinite State Black-Box Machine". All this opens the way to\nthe possibility of designing a new class of universal quantum computing\narchitectures based on this coalgebraic formulation of QFT, as its ability of\nnaturally generating a Fibonacci progression demonstrates.\n

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