Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory

Abstract

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined.

47 pages, no figures, ams-latex

References in corpus (3)

• Modular Structure and Duality in Conformal Quantum Field Theory
• Group Cohomology, Modular Theory and Space-time Symmetries
• On the manifestations of particles

Cited by in corpus (63)

• On the Renormalization Group in Curved Spacetime
• Algebraic Holography
• The Role of Type III Factors in Quantum Field Theory
• Generalized entropy for general subregions in quantum gravity
• Notes on the type classification of von Neumann algebras
• The Necessity of the Hadamard Condition
• How is quantum information localized in gravity?
• Combinatorics of (perturbative) quantum field theory
• Gravitational splitting at first order: Quantum information localization in gravity
• Phase space properties and the short distance structure in quantum field theory
• Quantum-first gravity
• Hilbert space structure in quantum gravity: an algebraic perspective
• The Quest for Understanding in Relativistic Quantum Physics
• Quarks, gluons, colour: Facts or fiction?
• Dynamical locality of the free scalar field
• State independence for tunneling processes through black hole horizons and Hawking radiation
• Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples
• On the manifestations of particles
• Real-space RG, error correction and Petz map
• Quantum Inequalities from Operator Product Expansions
• Phase Space Properties of Local Observables and Structure of Scaling Limits
• Noncommuting local common causes for correlations violating the Clauser-Horne inequality
• Constructive Field Theory and Applications: Perspectives and Open Problems
• Scaling limits of integrable quantum field theories
• Remarks on Causality in Relativistic Quantum Field Theory
• Scaling limits of lattice quantum fields by wavelets
• Semifinite von Neumann algebras in gauge theory and gravity
• Localization and Entanglement in Relativistic Quantum Physics
• Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
• Fluctuation Operators and Spontaneous Symmetry Breaking
• The Principle of Locality. Effectiveness, fate and challenges
• Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories
• On dilation symmetries arising from scaling limits
• Scaling Algebras and Superselection Sectors: Study of a Class of Models
• Massless relativistic wave equations and quantum field theory
• Quantum massless field in 1+1 dimensions
• Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Charges in the UV completion of neutral electrodynamics
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Structure functions of the 2d O(n) non-linear sigma models
• Perturbative Algebraic Field Theory, and Deformation Quantization
• Reminiscences about Many Pitfalls and Some Successes of QFT Within the Last Three Decades
• The Schmidt rank for the commuting operator framework
• Euclidean field theory on a sphere
• Structure functions of 2d integrable asymptotically free models
• Localizable Particles in the Classical Limit of Quantum Field Theory
• Extensions of Bundles of C*-algebras
• Spin and Statistics and First Principles
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models
• On the mixing property for a class of states of relativistic quantum fields
• Nuclearity and split for thermal quantum field theories
• Scaling algebras, the renormalization group and the principle of local stability in algebraic quantum field theory
• Application of Tomita-Takesaki theory in algebraic euclidean field theories
• Scaling Limit and Renormalisation Group in General (Quantum) Many Body Theory
• Linearization (in)stabilities and crossed products
• The Structure of Charges in the Ultraviolet and an Intrinsic Notion of Confinement
• A Gromov-Hausdorff Distance between von Neumann Algebras and an Application to Free Quantum Fields
• Scaling Analysis and Renormalisation Group for General (Quantum) Many Body Systems in the Critical Regime
• Short-distance analysis for algebraic euclidean field theory
• Constructive aspects of algebraic euclidean field theory
• Infinite volume limits in Euclidean quantum field theory via stereographic projection
• Renormalization Group Flow in Algebraic Holography