Braided quantum field theories and their symmetries

Abstract

Braided quantum field theories proposed by Oeckl can provide a framework for defining quantum field theories having Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We discuss Hopf algebra symmetries and such relations in braided quantum field theories. We give the four algebraic conditions between Hopf algebra symmetries and braided quantum field theories, which are required for the relations to hold. As concrete examples, we apply our discussions to the Poincare symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled with spinless particles given by Freidel and Livine, and the other is noncommutative field theory on Moyal plane. We also comment on quantum field theory on kappa-Minkowski spacetime.

36 pages, 18 figures, a comment added and typos corrected

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Cited by in corpus (23)

• Diffeomorphisms in group field theories
• Multi-orientable Group Field Theory
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Fractional and noncommutative spacetimes
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Quantum Fields with Noncommutative Target Spaces
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Infinity Operads and Monoidal Categories with Group Equivariance
• Braided Symmetries in Noncommutative Field Theory
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Duality and Braiding in Twisted Quantum Field Theory
• Tensor models and 3-ary algebras
• The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• UV/IR mixing as a twisted Poincaré anomaly
• Homotopy Lie Algebras of Gravity and their Braided Deformations
• Massive particles coupled with 2+1 dimensional gravity and noncommutative field theory
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Weighting bubbles in group field theory
• T-Minkowski noncommutative spacetimes II: classical field theory
• On the Correspondence between Poincaré Symmetry of Commutative QFT and Twisted Poincaré Symmetry of Noncommutative QFT
• Noncommutative scalar fields in compact spaces: quantisation and implications
• Non-commutative waves for gravitational anyons