Quantum groups and quantum field theory: I. The free scalar field
Abstract
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular structures can be built from the two-point function and the Feynman propagator of scalar fields to reproduce the operator product and the time-ordered product as twist deformations of the normal product. A correspondence is established between the quantum group and the quantum field concepts. On the mathematical side the underlying structures come out of Hopf algebra cohomology.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.