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Quantum field theory, connected.
Build a working understanding of quantum field theory—from first principles to the questions shaping research.
Search concepts, notation, and calculationsCtrl/⌘ KThe library 16 volumes
One field. Many perspectives.
From mathematical foundations to quantum gravity. Explore in any order, or find a guided path.
Mathematical Methods
The mathematical tools of field theory: distributions, geometry, topology, complex analysis, and the structures behind physical calculations.
Foundations of Quantum Field Theory
Understand quantum fields, states, observables, and particles, and how different formulations describe the same physical questions.
Symmetry and Gauge Structure
Explore symmetries, conserved currents, gauge redundancy, and anomalies, from familiar transformations to defects and generalized symmetries.
Perturbative QFT and Scattering
Calculate scattering amplitudes and measurable cross sections, connecting Feynman diagrams with unitarity, analyticity, and infrared physics.
Renormalization and Effective Field Theory
Follow physics across scales through renormalization, running couplings, effective theories, and systematic estimates of approximation errors.
Gauge Theories and the Standard Model
Study QED, QCD, and electroweak theory, connecting gauge interactions to particle phenomenology and precision tests.
Nonperturbative Dynamics
Investigate strong interactions beyond perturbation theory through solitons, instantons, integrability, functional methods, and controlled approximations.
Lattice and Hamiltonian QFT
Compute field theories with lattice and Hamiltonian methods, from Monte Carlo calculations to tensor networks and quantum simulation.
Conformal Field Theory and Bootstrap
Use conformal symmetry and consistency conditions to understand critical phenomena and constrain strongly interacting quantum field theories.
Supersymmetry and Duality
Explore supersymmetric theories, exact observables, and dual descriptions that reveal connections between apparently different quantum systems.
Thermal and Nonequilibrium QFT
Describe fields at finite temperature and density, and follow nonequilibrium dynamics from microscopic interactions to transport and hydrodynamics.
Many-Body QFT and Quantum Matter
Connect microscopic quantum systems to collective behavior, emergent fields, ordered phases, and topological forms of matter.
Quantum Information in QFT
Study entanglement, entropy, quantum channels, and information bounds in field theory, with their physical and mathematical limitations.
QFT in Curved Spacetime
Understand quantum fields in curved spacetime, including particle creation, horizon effects, cosmological evolution, and semiclassical gravity.
Holography and Quantum Gravity
Explore holographic duality, black holes, and quantum gravity, distinguishing established results from conjectures and open problems.
Mathematical QFT
Examine the mathematical foundations of quantum field theory through axioms, operator algebras, constructive methods, and rigorous existence questions.
Build the free scalar field from oscillator modes, recover its commutators, and see how particle excitations arise.
Background: Klein–Gordon modes and canonical commutators.
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