From first principles to current research
Quantum field theory, connected.
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Browse by subject, from mathematical methods to quantum gravity. For a guided reading sequence, start in Learn.
Mathematical Methods
Provide just-in-time, hypothesis-aware mathematics with immediate QFT applications and explicit exits to the owning physics or rigorous treatment.
Open volumeFoundations of Quantum Field Theory
Establish what quantum fields, states, observables, particles, formulations, and interacting limits mean, and show how physical information is encoded without treating formal notation as a definition.
Open volumeSymmetry and Gauge Structure
Build a convention-aware physical theory of symmetry in QFT—from actions, currents, Ward identities, backgrounds, breaking, and gauge redundancy through boundaries, BRST/BV, anomalies, defects, generalized symmetry, topological response, and symmetry TFT—while making every global, regulator, boundary, and categorical assumption visible.
Open volumePerturbative QFT and Scattering
Turn local interacting QFT data into convention-explicit perturbative amplitudes and infrared-safe observables, then expose the unitarity, analyticity, singularity, and evidence structure that makes those predictions physically interpretable.
Open volumeRenormalization and Effective Field Theory
Explain how local QFT remains predictive across scales: construct finite renormalized quantities, derive and validate RG flow, build systematically improvable effective theories, and expose the scheme, basis, matching, factorization and uncertainty contracts behind every result.
Open volumeGauge Theories and the Standard Model
Connect the structural language of gauge QFT to realized QED, Yang–Mills, QCD, nuclear, electroweak, flavor, neutrino, precision, and portal physics through convention-complete calculations, governed artifacts, and evidence claims that never outrun their source and validity contracts.
Open volumeNonperturbative Dynamics
Teach nonperturbative QFT as a hierarchy of controlled questions, exact structures, validated approximations, regulated evidence, and explicitly open problems—from vacua and saddles through strong dynamics, functional equations, resurgence, integrability, and rigorous-status handoffs.
Open volumeLattice and Hamiltonian QFT
Teach lattice, Hamiltonian, light-front, truncation, tensor-network, and quantum-simulation formulations as controlled routes from a regulated theory to continuum observables, with every statistical, systematic, computational, and evidence limitation explicit.
Open volumeConformal Field Theory and Bootstrap
Develop conformal QFT as a subject, a universal language of fixed points, and a nonperturbative solution strategy through convention-controlled CFT data and exact consistency conditions.
Open volumeSupersymmetry and Duality
Develop supersymmetry as an algebraic, dynamical, and computational structure and field-theory duality as a hypothesis-explicit equivalence claim, from finite cohomological models through exact observables and protected interfaces.
Open volumeThermal and Nonequilibrium QFT
Develop equilibrium, finite-density, real-time, stochastic, kinetic, hydrodynamic, open-system, hot-gauge, and QCD-collision field theory as one scale-, convention-, evidence-, and validity-aware framework.
Open volumeMany-Body QFT and Quantum Matter
Explain how controlled reductions from microscopic quantum systems produce nonrelativistic fields, quasiparticles, collective modes, ordered and topological phases, emergent gauge structures, dynamical regimes, and evidence-qualified claims about quantum matter.
Open volumeQuantum Information in QFT
Explain how information is defined, bounded, transported, measured, protected, and inferred in continuum quantum field theory while separating intrinsic local-algebra structure, regulated constructions, causal operational tasks, and definition-sensitive proposals.
Open volumeQFT in Curved Spacetime
Teach quantum field theory when geometry, observer motion, horizons, cosmological evolution, or semiclassical gravitational response are part of the physical problem, with every claim typed by state, observable, renormalization prescription, approximation regime, evidence status, and canonical handoff.
Open volumeHolography and Quantum Gravity
Build a claim-disciplined cathedral of holography and quantum gravity in which every dictionary, observable, approximation, derivation, theorem, numerical result, proposal, alternative program, and empirical bound is typed by assumptions, regime, evidence, falsifier, uncertainty, and canonical handoff.
Open volumeMathematical QFT
Build the theorem-first capstone of QFT.org: every axiom, construction, reconstruction, comparison, existence statement, continuum claim, counterexample, and open problem is typed by objects, maps, domains, hypotheses, conclusion, converse status, proof or evidence level, physical owner, and dated frontier handoff.
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