Towards Quantum Field Theory in Categorical Quantum Mechanics

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.

In Proceedings QPL 2017, arXiv:1802.09737

References in corpus (2)

• An approach to nonstandard quantum mechanics
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Cited by in corpus (6)

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• An effect-theoretic reconstruction of quantum theory
• Light-Matter Interaction in the ZXW Calculus
• Quantum Field Theory in Categorical Quantum Mechanics
• Causality in Higher Order Process Theories
• S-matrix interpretation in categorical quantum mechanics