An inside view of the tensor product
Abstract
Given a vector-space which is the tensor product of vector-spaces and , we reconstruct and from the family of simple tensors within . In an application to quantum mechanics, one would be reconstructing the component subsystems of a composite system from its unentangled pure states. Our constructions can be viewed as instances of the category-theoretic concepts of functor and natural isomorphism, and we use this to bring out the intuition behind these concepts, and also to critique them. Also presented are some suggestions for further work, including a hoped-for application to entanglement entropy in quantum field theory.
Cite
@article{arxiv.2303.14596,
title = {An inside view of the tensor product},
author = {Rafael D. Sorkin},
journal= {arXiv preprint arXiv:2303.14596},
year = {2023}
}
Comments
plainTeX, 29 pages. To appear in: Particles, Fields and Topology, Celebrating A.P. Balachandran, edited by T.R. Govindrajan, et al (World Scientific, Singapore). Most current version will be available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/ (or wherever my home-page may be)