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Categorical Quantum Mechanics - DOAJ

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Last Updated: 16 April 2022

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Infinite-dimensional Categorical Quantum Mechanics

We use non-standard methods to determine a category *Hilb suitable for categorical quantum mechanics in various separable Hilbert spaces, and we show that standard bounded operators can be appropriately embedded in it. We show the existence of unital special commutative dagger-Frobenius algebras, and we arrive at *Hilb is likely to be compact closed, with partial tracetraces and a Hilbert-Schmidt inner product on morphisms.

Source link: https://doi.org/10.4204/EPTCS.236.4


Towards Quantum Field Theory in Categorical Quantum Mechanics

In this work, we use techniques from non-standard analysis to create infinite-dimensional quantum devices and quantum fields within the framework of Categorical Quantum Mechanics. We're not sure about this, but we demonstrate how certain non-separable Hilbert spaces can also be modelled in our non-standard framework, and we explicitly discuss quantum fields on cubic lattices and quantum fields in real space.

Source link: https://doi.org/10.4204/EPTCS.266.22


Quantum Field Theory in Categorical Quantum Mechanics

Within the framework of categorical quantum mechanics, we use techniques from non-standard research to design the building blocks of quantum field theory. We design an object of *Hilb with quantum fields as states, and we show that the common ladder and field operators can be specified as acceptable endomorphisms, based on previous research.

Source link: https://doi.org/10.4204/EPTCS.287.9

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions