Academic Knowledge Base & Synthesis

Mathematical Proofs & Technical Notes

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Pedagogical expositions, graduate lecture monographs (including Cambridge lecture series by Prof. David Tong), complete course lecture notes, and mathematical derivations formatted with real-time KaTeX LaTeX equation rendering.

Theoretical physics chalkboard derivations, geometric formulas, and mathematical notation
6 Reference Collections & Monographs · 33 linked lecture PDFs
physics
August 202538 Lectures (Complete Course)

Quantum Field Theory I — Complete Lecture Notes Collection

Comprehensive 38-lecture course notes covering Classical Field Theory, Klein-Gordon & Dirac Fields, Canonical Quantization, Symmetries, Wick's Theorem, Feynman Rules, and Tree-Level Quantum Electrodynamics.

Includes 33 Handout Lecture Notes (PDFs)
33 lecture PDFs
#QuantumFieldTheory#CanonicalQuantization#DiracEquation#FeynmanDiagrams#QED#NoetherTheorem#ScatteringTheory
Direct PDF
physics
Cambridge Lecture NotesComplete Monograph (218 Pages)

String Theory — Lectures by David Tong

Prof. David Tong•University of Cambridge (DAMTP)

Celebrated Cambridge Part III lecture notes on bosonic string theory, covering classical actions, lightcone & covariant quantization, 2D Conformal Field Theory, Ghost systems, D-branes, and T-duality.

#StringTheory#ConformalFieldTheory#PolyakovAction#VirasoroAlgebra#DBranes#DavidTong#CambridgeDAMTP
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physics
Cambridge Lecture NotesComplete Monograph (140 Pages)

Particle Physics — Lectures by David Tong

Prof. David Tong•University of Cambridge (DAMTP)

Pedagogical Cambridge Part II lecture notes on particle physics, the quark model, Lie groups SU(2) & SU(3), hadron spectroscopy, Deep Inelastic Scattering, and the weak interaction.

#ParticlePhysics#QuarkModel#CKMMatrix#WeakInteractions#DeepInelasticScattering#DavidTong#CambridgeDAMTP
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physics
Cambridge Lecture NotesComplete Monograph (242 Pages)

The Standard Model — Lectures by David Tong

Prof. David Tong•University of Cambridge (DAMTP)

Comprehensive Cambridge Part III graduate monograph on Yang-Mills gauge theories, Quantum Chromodynamics, Electroweak Unification SU(2)xU(1), Spontaneous Symmetry Breaking, the Higgs mechanism, and chiral anomalies.

#StandardModel#YangMillsTheory#HiggsMechanism#ElectroweakUnification#QCD#DavidTong#CambridgeDAMTP
Direct PDF
physics
Cambridge Lecture NotesComplete Monograph (220 Pages)

Quantum Field Theory — Lectures by David Tong

Prof. David Tong•University of Cambridge (DAMTP)

Renowned Cambridge Part III introductory monograph on Quantum Field Theory covering classical fields, scalar field quantization, interacting fields, Wick's theorem, the Dirac equation, and Quantum Electrodynamics.

#QuantumFieldTheory#CanonicalQuantization#DiracEquation#FeynmanDiagrams#QED#DavidTong#CambridgeDAMTP
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physics
arXiv:gr-qc/9712019Complete Monograph (238 Pages)

Lecture Notes on General Relativity — Sean M. Carroll

Prof. Sean M. Carroll•Institute for Theoretical Physics, UC Santa Barbara

Comprehensive 238-page graduate pedagogical monograph on General Relativity covering special relativity, smooth manifolds, differential forms, curvature, Einstein field equations, gravitational radiation, Schwarzschild & Kerr black holes, and modern cosmology.

#GeneralRelativity#DifferentialGeometry#CurvatureTensors#EinsteinEquations#BlackHoles#Schwarzschild#KerrMetric#GravitationalWaves#Cosmology#SeanCarroll#arXiv
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