2007/04/30 by Yuya Sasai, Naoki Sasakura
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1143/ptp.118.785
published as Prog.Theor.Phys.118:785-814,2007 · 36 pages, 18 figures, a comment added and typos corrected
arxiv created 2007/08/27 · openalex publication_date 2007/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided quantum field theories that are required for the relations to hold. As concrete examples, we apply our analysis to the Poincaré symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled to spinless particles formulated by Freidel and Livine, and the other is noncommutative field theory on the Moyal plane. We also comment on quantum field theory in κ-Minkowski spacetime.