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Quantum Physics

arXiv:1703.09594v3 (quant-ph)
[Submitted on 28 Mar 2017 (v1), last revised 2 Mar 2018 (this version, v3)]

Title:Towards Quantum Field Theory in Categorical Quantum Mechanics

Authors:Stefano Gogioso (University of Oxford), Fabrizio Genovese (University of Oxford)
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Abstract: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.
Comments: In Proceedings QPL 2017, arXiv:1802.09737
Subjects: Quantum Physics (quant-ph); Category Theory (math.CT)
Cite as: arXiv:1703.09594 [quant-ph]
  (or arXiv:1703.09594v3 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1703.09594
Journal reference: EPTCS 266, 2018, pp. 349-366
Related DOI: https://doi.org/10.4204/EPTCS.266.22

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 28 Mar 2017 14:17:02 UTC (40 KB)
[v2] Sat, 15 Apr 2017 22:42:41 UTC (43 KB)
[v3] Fri, 2 Mar 2018 03:54:03 UTC (38 KB)
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