Notes an tagged vector space
arXiv:2510.17327
Abstract
A generalisation is provided for the notion of tags, often found in physics notation. The properties of tags and their extractors are discussed. It leads to the definition of tagged vector spaces. It is applied in the context of quantum optics, to provide a mathematical description for Dirac notation as used in physics. The commutation relations for ladder operators and a symplectic phase space are derived as consequences of the properties of tagged vector spaces. To incorporate the spatiotemporal and spin degrees of freedom, tags are indexed by functions, leading to a functional representation.