Quantum field theory and Hopf algebra cohomology
Abstract
We exhibit a Hopf superalgebra structure of the algebra of field operators of quantum field theory (QFT) with the normal product. Based on this we construct the operator product and the time-ordered product as a twist deformation in the sense of Drinfeld. Our approach yields formulas for (perturbative) products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods. Employing Hopf algebra cohomology sheds new light on the structure of QFT and allows the extension to interacting (not necessarily perturbative) QFT. We give a reconstruction theorem for time-ordered products in the spirit of Streater and Wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle. We also demonstrate how non-trivial vacua are described in our approach solving a problem in quantum chemistry.
Keywords
Cite
@article{arxiv.hep-th/0311253,
title = {Quantum field theory and Hopf algebra cohomology},
author = {Christian Brouder and Bertfried Fauser and Alessandra Frabetti and Robert Oeckl},
journal= {arXiv preprint arXiv:hep-th/0311253},
year = {2008}
}
Comments
39 pages, no figures, LaTeX + AMS macros; title changed, minor corrections, references updated