Rafael D. Sorkin
Published 2023-03-26Version 1
Given a vector-space $~V~$ which is the tensor product of vector-spaces $A$ and $B$, we reconstruct $A$ and $B$ from the family of simple tensors $a{\otimes}b$ within $V$. 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.
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)
Is quantum field theory a generalization of quantum mechanics?
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
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