The Operator Product Expansion in Quantum Field Theory

Abstract

Operator product expansions (OPEs) in quantum field theory (QFT) provide an asymptotic relation between products of local fields defined at points $x_1,\dots ,x_n$ and local fields at point $y$ in the limit $x_1,\dots ,x_n\to y$. They thereby capture in a precise way the singular behavior of products of quantum fields at a point as well as their ``finite trends.'' In this article, we shall review the fundamental properties of OPEs and their role in the formulation of interacting QFT in curved spacetime, the ``flow relations'' in coupling parameters satisfied by the OPE coefficients, the role of OPEs in conformal field theories, and the manner in which general theorems -- specifically, the PCT theorem -- can be formulated using OPEs in a curved spacetime setting.

arXiv comment20pp; article prepared for Encyclopedia of Mathematical Physics

References in corpus (25)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Spinning Conformal Blocks
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Bootstrapping Mixed Correlators in the 3D Ising Model
• OPE Convergence in Conformal Field Theory
• Carving Out the Space of 4D CFTs
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Axiomatic quantum field theory in curved spacetime
• Radial expansion for spinning conformal blocks
• Casimir recursion relations for general conformal blocks
• Categorification and correlation functions in conformal field theory
• The operator product expansion for perturbative quantum field theory in curved spacetime
• A General PCT Theorem for the Operator Product Expansion in Curved Spacetime
• The operator product expansion converges in perturbative field theory
• Action principle for OPE
• Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT
• Recursive construction of operator product expansion coefficients
• Associativity of the operator product expansion

Cited by in corpus (2)

• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Gravitational null rays: Covariant Quantization and the Dressing Time