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Towards Quantum Field Theory in Categorical Quantum Mechanics

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arxiv 1703.09594 v3 pith:2UL677BQ submitted 2017-03-28 quant-ph math.CT

Stefano Gogioso (University of Oxford) , Fabrizio Genovese (University of Oxford) This is my paper · ORCID
classification quant-phmath.CT
keywords quantumfieldsparticlescategoricalcubicframeworklatticesmechanics
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In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category *Hilb suitable for the algebraic manipulation of unbounded operators, Dirac deltas and plane-waves. We cover in detail the construction of quantum systems for particles in boxes with periodic boundary conditions, particles on cubic lattices, and particles in real space. Not quite satisfied with this, we show how certain non-separable Hilbert spaces can also be modelled in our non-standard framework, and we explicitly treat the cases of quantum fields on cubic lattices and quantum fields in real space.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension

    quant-ph 2022-07 unverdicted novelty 7.0 of 10

    Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.

  2. Quantum Information Flow under String-Diagram Rewriting

    quant-ph 2026-08 conditional novelty 6.0 of 10

    The authors define Coecke flow lines as branch-independent paths through quantum protocol diagrams that survive every semantics-preserving rewrite down to a bare wire.

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