Quantum Field Theory in Categorical Quantum Mechanics

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ID: 101756
2019
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Abstract
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as states and we show that the usual ladder and field operators can be defined as suitable endomorphisms. We deal with relativistic normalisation and we obtain the Lorentz invariant Heisenberg picture operators. By moving to a coherent perspective—where the classical time and momentum parameters are replaced by wavefunctions over the parameter spaces—we show that ladder operators and field operators can be obtained by applying the same morphism to plane waves and delta functions respectively. Finally, we formulate the commutation relations diagrammatically and we use them to derive the propagator.
Reference Key
gogioso2019quantumelectronic Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Gogioso, Stefano;Genovese, Fabrizio;
Journal electronic proceedings in theoretical computer science
Year 2019
DOI
DOI not found
URL
http://arxiv.org/pdf/1805.12087v2
Keywords
Medicine Technology (General) Chemical technology Biotechnology Science (General) Science physics environmental engineering earthwork. foundations mathematics electronic computers. computer science astrophysics inorganic chemistry

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