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Advanced
Quantum Field Theory
From the Klein-Gordon field to the Standard Model — a complete graduate curriculum synthesizing Peskin & Schroeder, Zee, and Srednicki, with interactive exercises, worked examples at every step, and the full mathematical depth the subject deserves.
22Topics
6Parts
100+Worked Examples
3Textbooks Synthesized
Why learn QFT here?
Textbooks are complete but slow. Lectures are fast but non-interactive. This is neither.
Three textbooks synthesized
Peskin & Schroeder, Zee, and Srednicki — the best from each, in one linear path.
Problem-first pedagogy
Every topic opens with a worked example and closes with exercises you solve yourself.
Full mathematical depth
No hand-waving. Every divergence is regulated. Every renormalization is carried out.
Built for exam prep
Qualifying exam-style problems with complete solutions in every section.
Prerequisites
QFT is a graduate-level subject. Before starting, you should be comfortable with:
Quantum Mechanics
Schrödinger eq., operators, spin
Special Relativity
Four-vectors, Lorentz invariance
Classical Field Theory
Lagrangians, Noether's theorem
The Curriculum
22 topics organized into six progressive parts — the fastest path from zero to the Standard Model.
I
The Foundations
Quantize classical fields. Build Fock space. Meet creation operators, the vacuum, and the propagator.
1
The Klein-Gordon Field
Quantize a scalar field, build Fock space from the vacuum, and derive the Feynman propagator.
→
4
Dirac's Equation
Relativistic quantum mechanics for spin-½ particles: the Dirac equation, spinors, antimatter, and chiral structure.
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5
The Quantized Dirac Field
Second quantization of fermions — anticommutation, the Dirac propagator, and the Spin-Statistics theorem.
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6
Path Integrals in Field Theory
Feynman's sum-over-histories, generating functionals, Gaussian integration, and the free propagator.
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II
Feynman Diagrams & QED
Add interactions, derive the Feynman rules, and calculate real QED cross sections from first principles.
7
Interacting Fields & Perturbation Theory
λφ⁴ theory, Wick's theorem, vacuum bubbles, and the bridge from Lagrangian to Feynman diagrams.
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2
Feynman Rules
Propagators, vertex factors, symmetry factors, and the systematic rules for computing any amplitude.
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8
Quantum Electrodynamics
The photon field, gauge invariance, minimal coupling, and the complete QED Lagrangian.
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9
Scattering in QED
e⁺e⁻ → μ⁺μ⁻, Compton scattering, trace technology, and the Klein-Nishina formula.
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III
Loops & Renormalization
Go beyond tree level — tame UV divergences, absorb them into parameters, and discover running couplings.
10
Radiative Corrections
One-loop diagrams, the electron self-energy, vacuum polarization, and the anomalous magnetic moment g−2.
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11
Regularization
Taming UV divergences with dimensional regularization, degree of divergence, and renormalization schemes.
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12
Renormalization
Absorbing UV divergences into bare parameters — counterterms, schemes, and all-orders finiteness.
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13
The Renormalization Group
Beta functions, running couplings, Callan-Symanzik equation, and asymptotic freedom.
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IV
Symmetry
Noether's theorem, the Goldstone mechanism, and how symmetry breaking generates mass.
14
Symmetries & Conserved Currents
Noether's theorem, Ward-Takahashi identities, and symmetry as the organizing principle of QFT.
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15
Spontaneous Symmetry Breaking
Goldstone's theorem, the Mexican hat potential, and massless Nambu-Goldstone bosons.
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16
The Higgs Mechanism
Gauge bosons eating Goldstone bosons to become massive — and the discovery of the Higgs boson in 2012.
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V
Non-Abelian Gauge Theories
Yang-Mills theory, ghost fields, QCD, and the anomalies that constrain every consistent gauge theory.
17
Non-Abelian Gauge Theory
Yang-Mills theory, SU(N) structure constants, gluon self-interactions, and the origin of asymptotic freedom.
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18
Quantizing Gauge Theories
Faddeev-Popov ghosts, gauge fixing, BRST symmetry, and the unitarity of non-Abelian gauge theories.
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19
Quantum Chromodynamics
Color charge, 8 gluons, asymptotic freedom, confinement, and deep inelastic scattering.
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20
Anomalies
The chiral anomaly, ABJ triangle diagrams, π⁰→2γ, and anomaly cancellation in the Standard Model.
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VI
The Complete Theory
Electroweak unification, the full Standard Model, and the Wilsonian view of what QFT really means.
21
Electroweak Unification
SU(2)_L×U(1)_Y gauge theory, the Weinberg angle, and the prediction of W, Z, and neutral currents.
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3
The Standard Model
Gauge symmetries, particle content, and fundamental interactions.
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22
Effective Field Theory
Wilsonian EFT, integrating out heavy fields, operator expansion, and the SMEFT.
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Ready to quantize a field?
Begin with the Klein-Gordon field — the simplest relativistic quantum field — and build upward from there.
Start Part I →