Notes (Portuguese):

- Tópicos de Cosmologia;
- Introdução à Física de Hádrons e Quarks;
- Introdução ao formalismo da Relatividade Geral;
- Equações diferenciais ordinárias by J. Espinar, M. Viana, G. Goedert e H. Mesa;
- Tópicos de línguas;

Notes:

- The Physics of Inflation A Course for Graduate Students in Particle Physics and Cosmology by Daniel Baumann;
- Concepts in Theoretical Physics by Daniel Baumann;
- The conceptual basis of quantum field theory by Gerard ’t Hooft;
- Lectures on special relativity by Balša Terzić;
- Concepts in Astrophysics by Balša Terzić;
- Dynamics and Relativity by David Tong;
- Dynamics and Relativity by Stephen Siklos;
- Special Relativity by G. W. Gibbons;
- Lecture notes for Mathematical Physics by Joseph A. Minahan;
- Joe’s Relatively Small Book of Special Relativity by Joseph Minahan;
- Gravitation och Kosmologi Lecture Notes by Joseph Minahan;
- QFT1 Lecture Notes by Joseph Minahan;
- Classical Dynamics by David Tong;
- Lectures on Electromagnetism by David Tong;
- Electromagnetism Alan Macfarlane;
- Classical Electrodynamics by Konstantin Likharev;
- Applications of Quantum Mechanics by David Tong;
- Statistical Physics by David Tong;
- Kinetic Theory by David Tong;
- Quantum Field Theory by David Tong;
- String Theory by David Tong;
- TASI Lectures on Solitons by David Tong;
- Lectures on the Quantum Hall Effect by David Tong;

Landau and Lifshitz Course of Theoretical Physics:

- Mechanics;
- The Classical Theory of Fields;
- Quantum Mechanics: Non-Relativistic Theory;
- Relativistic Quantum Theory;
- Statistical Physics, Part 1;
- Fluid Mechanics;
- Theory of Elasticity;
- Electrodynamics of Continuous Media;
- Statistical Physics, Part 2;
- Physical Kinetics;

Others:
- General Physics, Mechanics and Molecular Physics;
- Physics for Everyone, book 1;
- Physics for Everyone, book 2;
- Lectures on Nuclear Theory;

Computation:

Softwares/programming languages/compiles:
- Git (Free and open source distributed version control system designed to handle everything from small to very large projects with speed and efficiency);
- Octave (High-level programming language for numerical computations);
- Julia language (High-level, high-performance dynamic programming language for numerical computing);
- Sagemath (Mathematical software with features covering many aspects of mathematics);
- SageManifolds (SageMath towards differential geometry and tensor calculus);
- The R Project for Statistical Computing (Software environment for statistical computing);
- Python (High-level programming language for general-purpose programming);
- wxMaxima (System for the manipulation of symbolic and numerical expressions);
- GNU Compiler Collection (Front ends for C, C++, Objective-C, Fortran, Ada, Go, and D, as well as libraries for these languages (libstdc++,...));
- Perl (A highly capable, feature-rich programming language);
- Pandoc (A universal document converter);
- Gnu Regression, Econometrics and Time-series Library (Software package for econometric analysis);
- Langage Objet pour la RElativité NumériquE (C++ classes to solve various problems arising in numerical relativity);
- FLASH code (High performance application code);
- Jupyter (A language-agnostic web-based interactive shell/notebook server);
- Astropy (A community python library for astronomy);
- Make (GNU make utility to maintain groups of programs);
- Einstein Toolkit (Community-driven software platform of core computational tools in relativistic astrophysics and gravitational physics);
- PLUTO (Code for Astrophysical GasDynamics);
- FFTW (A library for computing the discrete Fourier transform);
- OpenBLAS (An optimized BLAS library based on GotoBLAS2 1.13 BSD);
- ROOT (C++ data analysis framework and interpreter from CERN);
- CUDA (NVIDIA's GPU programming toolkit);
- LAPACK (Linear Algebra PACKage);
- SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers);
- Open MPI (High performance message passing library);
- GSL (GNU modern numerical library for C and C++ programmers);
- Doxygen (Standard tool for generating documentation);
- LaTeX (A document preparation system);
- Chombo (Software for Adaptive Solutions of Partial Differential Equations);
- RAMSES-GPU (General-purpose Hydrodynamics (HD) and Magneto-hydrodynamics (MHD) simulation code);
- SpECTRE (Open-source code for multi-scale, multi-physics problems in astrophysics and gravitational physics);
- AMREX (A suite of Open astrophysical hydrodynamics codes for exascale architectures);

Plots:
- Gnuplot (Portable command-line driven graphing utility for Linux);
- Inkscape (Vector graphics editor);
- Engauge Digitizer (Extracts data points from images of graphs);
- Matplotlib (Python 2D plotting library which produces quality figures);
- GIMP (GNU Image Manipulation Program);

GNU/Linux distributions:
- Archlinux (Keep it simple, stupid);
- Debian (GNU/Linux computer operating system);
- LinuxMint (GNU/Linux distribution based on Debian and Ubuntu);
- Fedora (GNU/Linux distribution developed by the community);

Tutorials and informations online:
- PythonBooks (A variety of books about Python);
- FORTRAN Tutorial;
- Fortran Wiki (Aspects of the Fortran programming language);
- C++ Wiki (Aspects of the C++ programming language);
- Think Julia (How to Think Like a Computer Scientist);
- cplusplus.com (General information and tutorials about the C++ programming language);
- The home of Standard C++ on the web (News, status and discussion about the C++ standard on all compilers and platforms);

Interesting links:

- Site do professor Henrique Fleming;
- David Tong's webpage;
- How to become a GOOD Theoretical Physicist;
- The Theoretical Minimum;
- Notas para um Curso de Física-Matemática;
- The Feynman Lectures on Physics;
- Dynamics of the Universe in Problems;
- Professor global;
- Quantum Field Theory Lectures by Sidney R. Coleman;
- Instituto de Matemática Pura e Aplicada;

Random things:

- List of unsolved problems in physics;

Special Relativity:

  1. Spacetime coordinates, 4-vectors, metric tensor \(g_{\mu \nu}\), etc;
  2. Spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum, within of special relativity it relies on the Minkowski's geometry

    • Spacetime Coordinates:

      \( x^{\mu} = (ct, \vec{x}); \qquad x_{\mu} = (ct, -\vec{x}); \qquad \vec{x} = (x^{1}, x^{2}, x^{3}) = (x,y,z) \)
    • 4-Momentum:

      \( p^{\mu} = (E/c,\vec{p}); \qquad p_{\mu} = (E/c,-\vec{p}); \qquad \vec{p} = (p^{1}, p^{2}, p^{3}) = (p_x,p_y,p_z) \)
    • Ricci Tensor

      \( R_{\mu\nu} = \delta^{\sigma}{}_{\lambda} R^{\lambda}{}_{\mu \sigma \nu} \)
    • Schouten Tensor

      \( S_{\mu\nu} = \frac{1}{d-1} \, \left(R_{\mu\nu} - \frac{1}{2\,d}\,g_{\mu\nu} R \right) \)

      \( \nabla^{\nu} S_{\mu\nu} = \nabla_{\mu} S^{\nu}{}_{\nu} \)
    • Weyl Tensor

      \( C^{\lambda}{}_{\mu \sigma \nu} = R^{\lambda}{}_{\mu \sigma \nu} + g^{\lambda}{}_{\nu} \, S_{\mu \sigma} - g^{\lambda}{}_{\sigma} \, S_{\mu\nu} + g_{\mu\sigma} \, S^{\lambda}{}_{\nu} - g_{\mu\nu} \, S^{\lambda}{}_{\sigma} \)
    • Commutators of Covariant Derivatives

      \( \left[ \nabla_{\mu}, \nabla_{\nu} \right] A_{\lambda} = R_{\lambda \sigma \mu \nu} A^{\sigma} \)

      \( \left[ \nabla_{\mu}, \nabla_{\nu} \right] A^{\lambda} = R^{\lambda}{}_{\sigma \mu \nu} A^{\sigma} \)
    • Bianchi Identities

      \( \nabla_{\kappa} R_{\lambda \mu \sigma \nu} - \nabla_{\lambda} R_{\kappa \mu \sigma \nu} + \nabla_{\mu} R_{\kappa \lambda \sigma \nu} = 0 \)

      \( \nabla^{\nu} R_{\lambda \mu \sigma \nu} = \nabla_{\mu} R_{\lambda \sigma} - \nabla_{\lambda} R_{\mu\sigma} \)

      \( \nabla^{\nu} R_{\mu\nu} = \frac{1}{2} \, \nabla_{\mu} R \)
    • Bianchi Identities for the Weyl Tensor

      \( \nabla^{\nu} C_{\lambda \mu \sigma \nu} = \, (d-2) \, \left( \nabla_{\mu} S_{\lambda \sigma} - \nabla_{\lambda} S_{\mu \sigma} \right) \)

      \( \nabla^{\lambda} \nabla^{\sigma} C_{\lambda \mu \sigma \nu} = \frac{d-2}{d-1} \, \left[ \, \nabla^{2} R_{\mu\nu} - \frac{1}{2d} \, g_{\mu\nu} \nabla^{2} R - \frac{d-1}{2d} \, \nabla_{\mu} \nabla_{\nu} R \right. - \left. \left(\frac{d+1}{d-1}\right) \, R_{\mu}{}^{\lambda} R_{\nu \lambda} + C_{\lambda \mu \sigma \nu} R^{\lambda \sigma} + \frac{(d+1)}{d(d-1)} \, R \, R_{\mu\nu} + \frac{1}{d-1} \, g_{\mu\nu} \left(R^{\lambda\sigma} R_{\lambda \sigma} - \frac{1}{d} \, R^2 \right) \, \right] \)
    Conventions, Definitions, Identities, and Formulas:

    1. Curvature Tensors;
    2. Consider a \(d+1\) dimensional spacetime \((\mathcal{M},g)\). The covariant derivative \(\nabla\) is metric-compatible with \(g\)

      • Christoffel Symbols

        \( \Gamma^{\lambda}_{\,\mu\nu} = \frac{1}{2} g^{\lambda \rho}\left(\partial_{\mu} g_{\rho \nu} + \partial_{\nu} g_{\mu \rho} - \partial_{\rho} g_{\mu \nu}\right) \)
      • Riemann Tensor

        \( R^{\lambda}{}_{\mu\sigma\nu} = \partial_{\sigma} \Gamma^{\lambda}_{\, \mu\nu} - \partial_{\nu} \Gamma^{\lambda}_{\, \mu\sigma} + \Gamma^{\kappa}_{\,\mu\nu} \Gamma^{\lambda}_{\, \kappa \sigma} - \Gamma^{\kappa}_{\,\mu\sigma} \Gamma^{\lambda}_{\, \kappa \nu} \)
      • Ricci Tensor

        \( R_{\mu\nu} = \delta^{\sigma}{}_{\lambda} R^{\lambda}{}_{\mu \sigma \nu} \)
      • Schouten Tensor

        \( S_{\mu\nu} = \frac{1}{d-1} \, \left(R_{\mu\nu} - \frac{1}{2\,d}\,g_{\mu\nu} R \right) \)

        \( \nabla^{\nu} S_{\mu\nu} = \nabla_{\mu} S^{\nu}{}_{\nu} \)
      • Weyl Tensor

        \( C^{\lambda}{}_{\mu \sigma \nu} = R^{\lambda}{}_{\mu \sigma \nu} + g^{\lambda}{}_{\nu} \, S_{\mu \sigma} - g^{\lambda}{}_{\sigma} \, S_{\mu\nu} + g_{\mu\sigma} \, S^{\lambda}{}_{\nu} - g_{\mu\nu} \, S^{\lambda}{}_{\sigma} \)
      • Commutators of Covariant Derivatives

        \( \left[ \nabla_{\mu}, \nabla_{\nu} \right] A_{\lambda} = R_{\lambda \sigma \mu \nu} A^{\sigma} \)

        \( \left[ \nabla_{\mu}, \nabla_{\nu} \right] A^{\lambda} = R^{\lambda}{}_{\sigma \mu \nu} A^{\sigma} \)
      • Bianchi Identities

        \( \nabla_{\kappa} R_{\lambda \mu \sigma \nu} - \nabla_{\lambda} R_{\kappa \mu \sigma \nu} + \nabla_{\mu} R_{\kappa \lambda \sigma \nu} = 0 \)

        \( \nabla^{\nu} R_{\lambda \mu \sigma \nu} = \nabla_{\mu} R_{\lambda \sigma} - \nabla_{\lambda} R_{\mu\sigma} \)

        \( \nabla^{\nu} R_{\mu\nu} = \frac{1}{2} \, \nabla_{\mu} R \)
      • Bianchi Identities for the Weyl Tensor

        \( \nabla^{\nu} C_{\lambda \mu \sigma \nu} = \, (d-2) \, \left( \nabla_{\mu} S_{\lambda \sigma} - \nabla_{\lambda} S_{\mu \sigma} \right) \)

        \( \nabla^{\lambda} \nabla^{\sigma} C_{\lambda \mu \sigma \nu} = \frac{d-2}{d-1} \, \left[ \, \nabla^{2} R_{\mu\nu} - \frac{1}{2d} \, g_{\mu\nu} \nabla^{2} R - \frac{d-1}{2d} \, \nabla_{\mu} \nabla_{\nu} R \right. - \left. \left(\frac{d+1}{d-1}\right) \, R_{\mu}{}^{\lambda} R_{\nu \lambda} + C_{\lambda \mu \sigma \nu} R^{\lambda \sigma} + \frac{(d+1)}{d(d-1)} \, R \, R_{\mu\nu} + \frac{1}{d-1} \, g_{\mu\nu} \left(R^{\lambda\sigma} R_{\lambda \sigma} - \frac{1}{d} \, R^2 \right) \, \right] \)
    3. Differential Forms
      • p-Form Components

        \( {\bf A}_{(p)} = \frac{1}{p!}\,A_{\mu_1 \ldots \mu_p}\,dx^{\mu_1} \land \ldots \land dx^{\mu_p} \)
      • Exterior Derivative

        \( \Big(d{\bf A}_{(p)}\Big)_{\mu_1 \ldots \mu_{p+1}} = (p+1)\,\partial_{\,[\,\mu_1} A_{\mu_2 \ldots \mu_{p+1}\,]\,} \)

        \( B_{\,[\, \mu_1 \ldots \mu_n ]\,} := \frac{1}{n!}\,\Big(\,B_{\mu_1 \ldots \mu_n} + \textrm{permutations}\,\Big) \)
      • Hodge-Star

        \( \Big( \star {\bf A}_{(p)}\Big)_{\mu_1 \ldots \mu_{d+1-p}} = \frac{1}{p!}\,\epsilon_{\mu_1 \ldots \mu_{d+1-p}}{}^{\nu_1 \ldots \nu_p}\,A_{\nu_1 \ldots \nu_p} \)

        \( \star \,\star = \big(-1 \,\big)^{p\,(d+1-p)+1} \)
      • Wedge Product

        \( \Big( {\bf A}_{(p)} \land {\bf B}_{(q)} \Big)_{\mu_1 \ldots \mu_{p+q}} = \frac{(p+q)!}{p!\,q!}\,A_{\,[\,\mu_1 \ldots \mu_p} \, B_{\mu_{p+1} \ldots \mu_{p+q} \,]} \)
    4. Euler Densities
    5. Let \(\mathcal{M}\) be a manifold with dimension \(d+1 = 2n\) an even number. Our normalization gives \(\chi(S^{2n}) = 2\).
      • Curvature Two-Form

        \( \Big( {\bf A}_{(p)} \land {\bf B}_{(q)} \Big)_{\mu_1 \ldots \mu_{p+q}} = \frac{(p+q)!}{p!\,q!}\,A_{\,[\,\mu_1 \ldots \mu_p} \, B_{\mu_{p+1} \ldots \mu_{p+q} \,]} \)
      • The elliptical orbits of planets. The many body system
      • The action principle. Hamilton’s equations. The Lagrangean
      • The harmonic oscillator. The pendulum
      • Poisson’s brackets
      • Wave equations. Liquids and gases. The Navier-Stokes equations. Viscosity and friction
    6. Optics
      • Fraction and reflection
      • Lenses and mirrors
      • The telescope and the microscope
      • Introduction to wave propagation
      • Doppler effect
      • Huijgens’ principle of wave superposition
      • Wave fronts
      • Caustics
    7. Statistical Mechanics & Thermodynamics
      • The first, second and third laws of thermodynamics
      • The Boltzmann distribution
      • The Carnot cycle. Entropy. Heat engines
      • Phase transitions. Thermodynamical models
      • The Ising Model (postpone techniques to solve the 2-dimensional Ising Model to later)
      • Planck’s radiation law (as a prelude to Quantum Mechanics)
    8. Electronics
      • Ohm’s law, capacitors, inductors, using complex numbers to calculate their effects
      • Transistors, diodes
    9. Electromagnetism
      • Maxwell’s Theory for electromagnetism: Homogeneous and inhomogeneous
      • Maxwell’s laws in a medium. Boundaries. Solving the equations in: Vacumm and homogeneous medium (electromagnetic waves). In a box (wave guides). At boundaries (fraction and reflection)
      • The vector potential and gauge invariance (extremely important)
      • Emission and absorption on EM waves (antenna)
      • Light scattering against objects
    10. Computational Physics
    11. Quantum Mechanics (Non-relativistic)
      • Bohr’s atom
      • DeBroglie’s relations (Energy-frequency, momentum-wave number)
      • Schrödinger’s equation (with electric potential and magnetic field)
      • Ehrenfest’s theorem
      • A particle in a box
      • The hydrogen atom, solved systematically. The Zeeman effect. Stark effect
      • The quantum harmonic oscillator
      • Operators: energy, momentum, angular momentum, creation and annihilation operators
      • Their commutation rules
      • Introduction to quantum mechanical scattering. The S-matrix. Radio-active decay
    12. Atoms & Molecules
      • Chemical binding
      • Orbitals
      • Atomic and molecular spectra
      • Emission and absorption of light
      • Quantum selection rules
      • Magnetic moments
    13. Solid State Physics
      • Crystal groups
      • Bragg reflection
      • Dielectric and diamagnetic constants
      • Bloch spectra
      • Fermi level
      • Conductors, semiconductors and insulators
      • Specific heat
      • Electrons and holes
      • The transistor
      • Superconductivity
      • Hall effect
    14. Nuclear Physics
      • Isotopes. Radio-activity. Fission and Fusion
      • Droplet model
      • Nuclear quantum numbers
      • Magic nuclei
      • Isospin
      • Yukawa theory
    15. Plasma Physics
      • Magnetohydrodynamics
      • Alfvén waves
    16. Advanced Mathematics
      • Group theory, and the linear representations of groups
      • Lie group theory
      • Vectors and tensors
      • More techniques to solve (partial) differential and integral equations
      • Extremum principle and approximation techniques based on that
      • Difference equations
      • Generating functions
      • Hilbert space
      • Introduction to the functional integral
    17. Special Relativity
      • The Lorentz transformation
      • Lorentz contraction, time dilatation
      • \(E=mc^2\)
      • 4-vectors and 4-tensors
      • Transformation rules for the Maxwell field
      • Relativistic Doppler effect
    18. Advanced Quantum Mechanics
      • Hilbert space
      • Atomic transitions
      • Emission and absorption of light
      • Stimulated emission
      • Density matrix
      • Interpretation of QM
      • The Bell inequalities
      • Towards relativistic QM: The Dirac equation, finestructure
      • Electrons and positrons
      • BCS theory for superconductivity
      • Quantum Hall effect
      • Advanced scattering theory
      • Dispersion relations
      • Perturbation expansion
      • WKB approximation, Extremum principle
      • Bose-Einstein condensation
      • Superliquid helium
    19. Phenomenology/Astroparticles
      • Subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays
    20. General Relativity
      • The metric tensor
      • Space-time curvature
      • Einstein’s gravity equation
      • The Schwarzschild black hole
      • Reissner-Nordström black hole
      • Periastron shift
      • Gravitational lensing
      • Cosmological models
      • Gravitational radiation
    21. Cosmology
    22. Astrophysics
    23. Quantum Field Theory
      • Classical fields: Scalar, Dirac-spinor, Yang-Mills vector fields
      • Interactions, perturbation expansion. Spontaneous symmetry breaking, Goldstone mode, Higgs mechanism
      • Particles and fields: Fock space. Antiparticles. Feynman rules. The Gell-Mann-Lévy sigma model for pions and nuclei. Loop diagrams. Unitarity, Causality and dispersion relations. Renormalization (Pauli-Villars; dimensional ren.) Quantum gauge theory: Gauge fixing, Faddeev-Popov determinant, Slavnov identities, BRST symmetry. The renormalization group. Asymptotic freedom.
      • Solitons, Skyrmions. Magnetic monopoles and instantons. Permanent quark confinement mechanism. The 1/N expansion. Operator product expansion. Bethe-Salpeter equation. Construction of the Standard Model. P and CP violation. The CPT theorem. Spin and statistics connection. Supersymmetry.
    24. Supersymmetry/Supergravity

    Copy of How to become a GOOD Theoretical Physicist:

    1. Languages;
      • English
      • Some French, German, Spanish and Italian may be useful too
    2. Primary Mathematics
      • Natural numbers
      • Integers
      • Rational numbers
      • Real numbers
      • Complex numbers
      • Set theory: open sets, compacts spaces. Topology
      • Algebraic equations. Approximations techniques. Series expansions: Taylor series
      • Solving equations with complex numbers. Trigonometry
      • Infinitesimals. Differentiation. Differentiate basic functions
      • Integration. Integrate basic functions. Differential equations. Linear equations
      • Fourier transformation. The use of complex numbers. Convergence of series
      • The complex plane. Cauchy theorems and contour integration
      • The gamma function
      • Gaussian integrals. Probability theory
      • Partial differential equations. Dirichlet and Neumann boundary conditions
    3. Classical Mechanics
      • Static mechanics (force, tension). Hydrostatics. Newton's Laws
      • The elliptical orbits of planets. The many body system
      • The action principle. Hamilton’s equations. The Lagrangean
      • The harmonic oscillator. The pendulum
      • Poisson’s brackets
      • Wave equations. Liquids and gases. The Navier-Stokes equations. Viscosity and friction
    4. Optics
      • Fraction and reflection
      • Lenses and mirrors
      • The telescope and the microscope
      • Introduction to wave propagation
      • Doppler effect
      • Huijgens’ principle of wave superposition
      • Wave fronts
      • Caustics
    5. Statistical Mechanics & Thermodynamics
      • The first, second and third laws of thermodynamics
      • The Boltzmann distribution
      • The Carnot cycle. Entropy. Heat engines
      • Phase transitions. Thermodynamical models
      • The Ising Model (postpone techniques to solve the 2-dimensional Ising Model to later)
      • Planck’s radiation law (as a prelude to Quantum Mechanics)
    6. Electronics
      • Ohm’s law, capacitors, inductors, using complex numbers to calculate their effects
      • Transistors, diodes
    7. Electromagnetism
      • Maxwell’s Theory for electromagnetism: Homogeneous and inhomogeneous
      • Maxwell’s laws in a medium. Boundaries. Solving the equations in: Vacumm and homogeneous medium (electromagnetic waves). In a box (wave guides). At boundaries (fraction and reflection)
      • The vector potential and gauge invariance (extremely important)
      • Emission and absorption on EM waves (antenna)
      • Light scattering against objects
    8. Computational Physics
    9. Quantum Mechanics (Non-relativistic)
      • Bohr’s atom
      • DeBroglie’s relations (Energy-frequency, momentum-wave number)
      • Schrödinger’s equation (with electric potential and magnetic field)
      • Ehrenfest’s theorem
      • A particle in a box
      • The hydrogen atom, solved systematically. The Zeeman effect. Stark effect
      • The quantum harmonic oscillator
      • Operators: energy, momentum, angular momentum, creation and annihilation operators
      • Their commutation rules
      • Introduction to quantum mechanical scattering. The S-matrix. Radio-active decay
    10. Atoms & Molecules
      • Chemical binding
      • Orbitals
      • Atomic and molecular spectra
      • Emission and absorption of light
      • Quantum selection rules
      • Magnetic moments
    11. Solid State Physics
      • Crystal groups
      • Bragg reflection
      • Dielectric and diamagnetic constants
      • Bloch spectra
      • Fermi level
      • Conductors, semiconductors and insulators
      • Specific heat
      • Electrons and holes
      • The transistor
      • Superconductivity
      • Hall effect
    12. Nuclear Physics
      • Isotopes. Radio-activity. Fission and Fusion
      • Droplet model
      • Nuclear quantum numbers
      • Magic nuclei
      • Isospin
      • Yukawa theory
    13. Plasma Physics
      • Magnetohydrodynamics
      • Alfvén waves
    14. Advanced Mathematics
      • Group theory, and the linear representations of groups
      • Lie group theory
      • Vectors and tensors
      • More techniques to solve (partial) differential and integral equations
      • Extremum principle and approximation techniques based on that
      • Difference equations
      • Generating functions
      • Hilbert space
      • Introduction to the functional integral
    15. Special Relativity
      • The Lorentz transformation
      • Lorentz contraction, time dilatation
      • \(E=mc^2\)
      • 4-vectors and 4-tensors
      • Transformation rules for the Maxwell field
      • Relativistic Doppler effect
    16. Advanced Quantum Mechanics
      • Hilbert space
      • Atomic transitions
      • Emission and absorption of light
      • Stimulated emission
      • Density matrix
      • Interpretation of QM
      • The Bell inequalities
      • Towards relativistic QM: The Dirac equation, finestructure
      • Electrons and positrons
      • BCS theory for superconductivity
      • Quantum Hall effect
      • Advanced scattering theory
      • Dispersion relations
      • Perturbation expansion
      • WKB approximation, Extremum principle
      • Bose-Einstein condensation
      • Superliquid helium
    17. Phenomenology/Astroparticles
      • Subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays
    18. General Relativity
      • The metric tensor
      • Space-time curvature
      • Einstein’s gravity equation
      • The Schwarzschild black hole
      • Reissner-Nordström black hole
      • Periastron shift
      • Gravitational lensing
      • Cosmological models
      • Gravitational radiation
    19. Cosmology
    20. Astrophysics
    21. Quantum Field Theory
      • Classical fields: Scalar, Dirac-spinor, Yang-Mills vector fields
      • Interactions, perturbation expansion. Spontaneous symmetry breaking, Goldstone mode, Higgs mechanism
      • Particles and fields: Fock space. Antiparticles. Feynman rules. The Gell-Mann-Lévy sigma model for pions and nuclei. Loop diagrams. Unitarity, Causality and dispersion relations. Renormalization (Pauli-Villars; dimensional ren.) Quantum gauge theory: Gauge fixing, Faddeev-Popov determinant, Slavnov identities, BRST symmetry. The renormalization group. Asymptotic freedom.
      • Solitons, Skyrmions. Magnetic monopoles and instantons. Permanent quark confinement mechanism. The 1/N expansion. Operator product expansion. Bethe-Salpeter equation. Construction of the Standard Model. P and CP violation. The CPT theorem. Spin and statistics connection. Supersymmetry.
    22. Supersymmetry/Supergravity