Quantum Field TheoryInteractive Learning Path

A full conceptual introduction to quantum field theory, following the opening lecture and explaining why modern physics moves from particles in space to quantum fields defined over spacetime.

A full introduction to the Hamiltonian formulation of classical field theory, showing how fields are treated as infinitely many coupled degrees of freedom with canonical variables, conjugate momenta, and Hamiltonian evolution.

A full introduction to canonical quantization for fields, showing how classical field variables become operators, why equal-time commutators are imposed, and how Fourier modes turn a free field into a continuum of quantum harmonic oscillators.

A full lecture reconstruction showing how particle language emerges from field states, how classical fields arise as coherent states, why particle definitions can be basis-dependent, and how charged fields naturally lead to antiparticles.

A full lecture reconstruction of the Casimir effect, following the original lecture's development from vacuum wave functionals and vacuum fluctuations to regularization, Euler–Maclaurin analysis, the large-plate asymptotics, and the final Casimir pressure formula.

A full lecture reconstruction on how charge emerges from field symmetries, how complex fields encode oppositely charged particles, and how bosonic and fermionic statistics arise from commutation and anti-commutation relations in quantum field theory.

A concise conceptual reconstruction showing how spin arises from the covariance principle as the intrinsic angular momentum associated with the rotation of a field’s internal orientation, distinct from orbital angular momentum which comes from rotating the field’s spatial pattern.

A full lecture reconstruction on how ordinary spin generalizes to relativistic quantum field theory through the Lorentz group, its generators, its reducibility into left- and right-handed sectors, and the emergence of Lorentz 2-spinors.

A full lecture reconstruction showing how the Dirac equation emerges from Lorentz 2-spinors, how left- and right-handed spinors are related by derivative and conjugation operations, how the Majorana equation appears as the neutral case, and how the charged spinor field leads to the standard 4-spinor Dirac equation.

A full lecture reconstruction on how the Dirac equation is embedded into quantum field theory through the Dirac Lagrangian, canonical momentum field, Hamiltonian, normal mode decomposition, fermionic quantization, and the resulting momentum and charge operators.

A full lecture reconstruction introducing classical Maxwell–Dirac theory from local U(1) gauge symmetry, deriving minimal coupling and continuity, and then motivating normal ordering and the nontrivial charge structure of the Dirac vacuum.

A full lecture reconstruction showing how a constant classical electric field causes electron-positron pair creation by reducing the Dirac-field evolution problem to independent Landau-Zener transitions for each momentum-spin mode pair.

A full lecture reconstruction showing how the inertial vacuum of a quantum field appears thermal to a uniformly accelerating observer, using a massless scalar field in 1+1 dimensions, two-mode squeezed states, Rindler coordinates, and the emergence of the Unruh temperature.

A full lecture reconstruction showing how the gauge-invariant Maxwell–Dirac Lagrangian leads, after constraints and gauge fixing, to the Hamiltonian formulation of electrodynamics in Coulomb gauge, with only the two transverse dynamical photon degrees of freedom remaining.

A full lecture reconstruction showing how the free electromagnetic field in Coulomb gauge becomes an infinite set of quantum harmonic oscillators whose quanta are photons, and why gauge-invariant observables still preserve relativistic causality in photon detection.

A full lecture reconstruction introducing perturbative quantum electrodynamics from the Coulomb-gauge Hamiltonian, identifying the fine-structure constant as the small expansion parameter, and using time-independent perturbation theory to analyze the QED vacuum and one-electron states.

A full lecture reconstruction showing why naive low-order perturbative QED corrections to particle energies are problematic, why Compton scattering is the first clean finite order-α process, and how Lorentz-invariant scattering amplitudes emerge only after coherent addition of all electron and positron intermediate-state processes.

A full lecture reconstruction introducing path integrals as a Lagrangian reformulation of quantum mechanics, starting from the Feynman–Hibbs phase-space path integral, then developing coherent-state path integrals for bosons and Grassmann coherent-state path integrals for fermions as preparation for Lagrangian perturbation theory in QFT.

A full lecture reconstruction showing how bosonic and fermionic coherent-state path integrals combine into the QED generating functional, and how changes of variables turn the Coulomb-gauge Hamiltonian path integral into a manifestly Lorentz-invariant Maxwell–Dirac action with sources.

A full lecture reconstruction showing how Lorentz-invariant perturbative QED emerges from the QED path integral as variational calculus on a Gaussian generating functional, and how the surviving terms organize into Feynman diagrams and Feynman rules.

A full lecture reconstruction showing how loop divergences arise in perturbative QED, why only three classes of divergent loop integrals survive, and how their effects can be absorbed into mass, charge, and field-strength renormalization.