Theoretical Physics Ph.D. Core
The Theorist's Path The Magnum Opus. A rigorous, chronological path from freshman calculus to the frontiers of String Theory and Quantum Gravity. Inspired by the legendary Landau theoretical minimum.
12 WEEKS
Mathematical Toolkit I The absolute prerequisites. You cannot do physics without fluency here.
Multivariable Calculus (Jacobians, Surface Integrals) Linear Algebra (Eigenvalues/Vectors, Diagonalization) Ordinary Differential Equations Vector Calculus (Div, Grad, Curl, Stokes' Thm) Complex Numbers & Euler's Formula Fourier Series & Transforms
14 WEEKS
Classical Mechanics The universe is deterministic... for now. The Principle of Least Action.
Lagrangian Formalism The Principle of Least Action Hamiltonian Mechanics & Phase Space Noether's Theorem & Conservation Laws Central Forces & Kepler Problem Coupled Oscillators & Normal Modes Poisson Brackets Canonical Transformations
12 WEEKS
Electromagnetism & Optics Fields, waves, and the nature of light.
Maxwell's Equations (Integral & Differential) Electrostatics & Multipole Expansion Magnetostatics & Vector Potential EM Waves in Matter & Conductors Poynting Vector & Energy Transport Reflection, Refraction, & Fresnel Equations Retarded Potentials
10 WEEKS
Mathematical Toolkit II Preparing for curved space and infinite dimensions.
Complex Analysis (Residue Theorem, Contour Integration) Partial Differential Equations (Separation of Variables) Special Functions (Bessel, Legendre, Hermite) Tensor Analysis (Intro) Hilbert Spaces Green's Functions
Milestone 16 WEEKS
Quantum Mechanics I Breaking the determinism of the universe.
The Wavefunction & Probability Interpretation Schrödinger Equation Quantum Harmonic Oscillator (Ladder Operators) Dirac Notation (Bra-Ket) Commutators & Uncertainty Principle The Hydrogen Atom Angular Momentum & Spin Stern-Gerlach Experiment
10 WEEKS
Statistical Mechanics From micro-states to macro-laws. The bridge between QM and Thermo.
Microcanonical, Canonical, & Grand Canonical Ensembles Entropy & Information Theory Partition Functions Bose-Einstein Condensation Fermi-Dirac Statistics Blackbody Radiation Ising Model & Phase Transitions
14 WEEKS
Relativistic Electrodynamics The covariate formulation of physics. The "Jackson" Course.
Minkowski Spacetime Geometry Covariant 4-Vectors Electromagnetic Field Tensor (F_mu_nu) Gauge Invariance (Lorenz/Coulomb) Liénard–Wiechert Potentials Synchrotron Radiation Bremsstrahlung
12 WEEKS
Quantum Mechanics II Approximation methods, scattering, and symmetries.
Time-Independent Perturbation Theory Variational Principle WKB Approximation Time-Dependent Perturbation Theory Fermi's Golden Rule Scattering Theory (Born Approx, Partial Waves) Berry Phase Aharonov-Bohm Effect
Milestone 16 WEEKS
General Relativity Gravity is geometry. Spacetime tells matter how to move.
Equivalence Principle Differential Geometry (Manifolds, Metrics) Geodesic Equation Riemann Curvature Tensor Einstein Field Equations Schwarzschild Black Holes Kerr Rotating Black Holes Gravitational Waves FLRW Cosmology
16 WEEKS
Quantum Field Theory I Particle physics is born. Combining QM and Special Relativity.
Klein-Gordon Field Dirac Field & Spinors Canonical Quantization Feynman Propagators Feynman Diagrams & Rules QED (Quantum Electrodynamics) Cross Sections & Decay Rates Renormalization (Intro)
16 WEEKS
Quantum Field Theory II Gauge theories, loops, and the Standard Model.
Path Integral Formulation Renormalization Group Flow Non-Abelian Gauge Theories (Yang-Mills) Spontaneous Symmetry Breaking Goldstone Bosons The Higgs Mechanism Chiral Anomalies QCD & Asymptotic Freedom
20 WEEKS
String Theory & M-Theory The candidate for the Theory of Everything.
Nambu-Goto & Polyakov Actions Bosonic String Quantization Conformal Field Theory (CFT) Superstrings (Type I, IIA, IIB, Heterotic) T-Duality D-Branes AdS/CFT Correspondence Compactification on Calabi-Yau Manifolds