Quantum fields, non-locality and quantum group symmetries

Abstract

We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be described within the usual framework of Lie algebras but rather in terms of non-co-commutative Hopf algebras or "quantum groups". Similar "quantizations" of space-time symmetries are expected to emerge in the low-energy limit of certain quantum gravity models and have been used to describe the symmetries of various non-commutative space-times. Our result provides an intuitive characterization of the mechanism that could lead to the emergence of deformed co-products in models of quantum relativistic symmetries.

12 pages, RevTeX, minor revisions, published version

References in corpus (17)

• The holographic principle
• Effective Field Theory, Black Holes, and the Cosmological Constant
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Observables in effective gravity
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• A Measure of de Sitter Entropy and Eternal Inflation
• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• Fock space, quantum fields and kappa-Poincaré symmetries
• A perturbative approach to Dirac observables and their space-time algebra
• An introduction to quantized Lie groups and algebras
• The Holographic Entropy Bound and Local Quantum Field Theory
• Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems

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• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity
• Rainbow statistics
• On kappa-deformation and triangular quasibialgebra structure
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Kinematics of a relativistic particle with de Sitter momentum space
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• On limitations of the extent of inertial frames in non-commutative relativistic spacetimes
• Field Theory on Curved Noncommutative Spacetimes
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• A bound on Planck-scale modifications of the energy-momentum composition rule from atomic interferometry
• Quantum particles in non-commutative space-time: an identity crisis
• Hidden entanglement at the Planck scale: loss of unitarity and the information paradox
• D3 branes in a Melvin universe: a new realm for gravitational holography
• Spacetime discreteness via consistent microscopic measurement