Lecture

Quantum Field Theory: Classification and Constraints

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture delves into the fundamentals of Quantum Field Theory (QFT), focusing on the classification of Conformal Field Theories (CFTs) in different dimensions and the constraints imposed by the S-matrix Bootstrap approach. The instructor explores the space of QFTs, from the classification of CFTs in 1+1 dimensions to the implications of Gravity as a path to QFT. Key topics include the Conformal Bootstrap, the holographic principle, and the AdS/CFT correspondence. Through scattering thought experiments and analytical tools, the lecture demonstrates how general principles like Lorentz invariance, causality, and unitarity shape the understanding of QFTs.

Official source

Related concepts (32)

Conformal field theory

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points.

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

Two-dimensional conformal field theory

A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations. In contrast to other types of conformal field theories, two-dimensional conformal field theories have infinite-dimensional symmetry algebras. In some cases, this allows them to be solved exactly, using the conformal bootstrap method. Notable two-dimensional conformal field theories include minimal models, Liouville theory, massless free bosonic theories, Wess–Zumino–Witten models, and certain sigma models.

Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group, known as the conformal group. The extension includes special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 degrees of freedom: ten for the Poincaré group, four for special conformal transformations, and one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations.

Liouville field theory

In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation. Liouville theory is defined for all complex values of the central charge of its Virasoro symmetry algebra, but it is unitary only if and its classical limit is Although it is an interacting theory with a continuous spectrum, Liouville theory has been solved. In particular, its three-point function on the sphere has been determined analytically.

Related lectures (64)

Weakly Coupled QFT in AdS

Explores weakly coupled quantum field theory in AdS, including state-operator correspondence and semiclassical gravity.

Dotsenko-Fateev Approach: Correlation Functions in Quantum Field Theory

Covers the Dotsenko-Fateev approach to computing correlation functions in quantum field theory.

Renormalization & Scaling

Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Quantum Field Theory in AdS: State-Operator Correspondence

Covers the study of free particle quantum mechanics in AdS and the State-Operator Correspondence in AdS.

Conformal Blocks: Functions on Moduli Spaces