2025/10/20 by Filippus S. Roux, Roux, Filippus S. · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.2510.17327
openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
A generalization is provided for the notion of tags, as used in various formulations of physical scenarios. It leads to the definition of tagged vector spaces, based on a set of axioms for tags and their extractors. As an application, such a tagged vector space is used to provide, in the context of quantum optics, a formal mathematical description for the Dirac notation that is closer to its intended usage compared to current mathematical formulations: it provides a one-to-one mapping between kets and bras and allows operators to operate either to the left or to the right. The canonical commutation relations for the quadrature and ladder operators are derived as consequences of the axioms of the tagged vector space. These axioms also lead to a symplectic phase space with the Wigner function and the Weyl transform emerging naturally.