Quantum field theory and Hopf algebra cohomology
arXiv:hep-th/0311253 · doi:10.1088/0305-4470/37/22/014
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.
39 pages, no figures, LaTeX + AMS macros; title changed, minor corrections, references updated
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- Combinatorial Hopf algebras in quantum field theory I
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- Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
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- Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple
- Combinatorics of n-point functions via Hopf algebra in quantum field theory
- Cliffordization, Spin and Fermionic Star Products
- Hopf-algebraic deformations of products and Wick polynomials
- Quantum field theory meets Hopf algebra
- Generating loop graphs via Hopf algebra in quantum field theory
- Tree expansion in time-dependent perturbation theory
- Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
- Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
- The Dirichlet Hopf algebra of arithmetics
- Hopf Algebras, Distributive (Laplace) Pairings and Hash Products: A unified approach to tensor product decompositions of group characters
- Super-bicharacter construction of quantum vertex algebras
- Many-body theory of degenerate systems
- From Quantum Mechanics to Quantum Field Theory: The Hopf route
- Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
- The Epstein-Glaser approach to pQFT: graphs and Hopf algebras