Table of Contents

1 Languages

English is a prerequisite. If you haven’t mastered it yet, learn it. You must be able to read, write, speak and understand English, but you don’t have to be perfect here. The lousy English used in this text is mine. That’s enough. All publications are in English. Note the importance of being able to write in English. Sooner or later you will wish to publish your results. People must be able to read and understand your stuff.

French, German, Spanish and Italian may be useful too, but they are not at all necessary. They are nowhere near the foundations of our sky-scraper, so don’t worry. You do need the Greek alphabet. Greek letters are used a lot. Learn their names, otherwise you make a fool of yourself when giving an oral presentation.

If you have managed to read and follow this webpage so far, you probably don’t need a first course in English. However, you want to be precise in your academic publications. You never want to be misunderstood, after all. Below, you will find several resources that are intended to be helpful for readers of various levels and with various requirements.

2 Primary Mathematics

Now, first things first. Are you comfortable with numbers, adding, subtracting, square roots, etc.?

  • Natural numbers: 1, 2, 3, …
  • Integers: …, -3, -2, -1, 0, 1, 2, …

  • Rational numbers (fractions): \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{3}{4}\), \(\frac{23791}{773}\), …

  • Real numbers: \(\sqrt{2} = 1.4142135\cdots\) , \(\pi = 3.14159265\cdots\) ,\(e = 2.7182818\cdots\), …

  • Complex numbers: 2+3i, \(e^{ia}= \cos(a) + i \sin(a)\), … they are very important! Set theory: open sets, compact spaces. Topology.You may be surprised to learn that they do play a role indeed in physics!

  • Algebraic equations. Approximation techniques. Series expansions: the Taylor series.
  • Solving equations with complex numbers. Trigonometry: \(\sin(2x)=2\sin x \cos x\), etc.
  • Infinitesimals. Differentiation. Differentiate basic functions (sin, cos, exp).
  • Integration. Integrate basic functions, when possible. Differential equations. Linear equations.
  • The Fourier transformation. The use of complex numbers. Convergence of series.
  • The complex plane. Cauchy theorems and contour integration (now this is fun).
  • The Gamma function (enjoy studying its properties).
  • Gaussian integrals. Probability theory.
  • Partial differential equations. Dirichlet and Neumann boundary conditions.

This is for starters. Some of these topics actually come as entire lecture courses. Much of those are essential ingredients of theories in Physics. You don’t have to finish it all before beginning with what follows next, but remember to return to those subjects skipped during the first round.

3 Classical Mechanics

  • Static mechanics (forces, tension); hydrostatics. Newton’s Laws
  • The elliptical orbits of planets. The many-body system
  • The action principle. Hamilton’s equations. The Lagrangean. (Don’t skip - extremely important!)
  • 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 and 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

(Only some very basic things about electronic circuits)

-Ohm’s law, capacitors, inductors, using complex numbers to calculate their effects -Transistors, diodes (how these actually work comes later)

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

Even the pure sang theorist may be interested in some aspects of 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 and 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
  • Supraconductivity
  • Hall effect

12 Nuclear Physics

  • Isotopes
  • Radio-activity
  • Fission and fusion
  • Droplet model
  • Nuclear quantum numbers
  • Magic nuclei
  • Isospin
  • Yukawa theory

13 Plasma Physics

  • Magneto-hydrodynamics
  • 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

17 Phenomenology

  • Subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays - - property of materials and chemistry
  • nuclear isotopes; phase transitions
  • astrophysics (planetary system, stars, galaxies, red shifts, supernovae)
  • cosmology (cosmological models, inflationary universe theories, microwave background radiation)
  • detection techniques.

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

Cosmology and Astrophysics are relatively young branches of science where a lot is happening. It is recommended to take notice of these important subjects, and devote time on them according to your taste. Indeed you must know that there is feedback from cosmology, astrophysics and astroparticle physics in solving various physics questions. But I can go on this way: what about the physics of other special branches of science: biophysics, geophysics, the physics of music, … I encourage you to search for other such subjects of interest on the web.

20 Astro-Physics and Astronomy

Cosmology and Astrophysics are relatively young branches of science where a lot is happening. It is recommended to take notice of these important subjects, and devote time on them according to your taste. Indeed you must know that there is feedback from cosmology, astrophysics and astroparticle physics in solving various physics questions. But I can go on this way: what about the physics of other special branches of science: biophysics, geophysics, the physics of music, … I encourage you to search for other such subjects of interest on the web.

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 and Supergravity

In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a field theory that combines the principles of supersymmetry and general relativity. In supergravity, supersymmetry is local (in contrast to non-gravitational supersymmetric theories, such as the Minimal Supersymmetric Standard Model). Since the generators of supersymmetry (SUSY) are convoluted with the Poincaré group to form a super-Poincaré algebra, it can be seen that gravity follows naturally from local supersymmetry.

23 Astro Particle Physics

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry “to ascertain the nature of the heavenly bodies, rather than their positions or motions in space.” Among the objects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background.Their emissions are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.

In practice, modern astronomical research often involves a substantial amount of work in the realms of theoretical and observational physics. Some areas of study for astrophysicists include their attempts to determine: the properties of dark matter, dark energy, and black holes; whether or not time travel is possible, wormholes can form, or the multiverse exists; and the origin and ultimate fate of the universe. Topics also studied by theoretical astrophysicists include: Solar System formation and evolution; stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics.

24 Super String Theory

Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.

‘Superstring theory’ is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity.

Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory.

25 Texts and Other resources

There are many more lecture notes to be found on the web. There are numerous good books on all sorts of topics in Theoretical Physics. Here are a few:

Classical Mechanics:

  • Classical Mechanics - 3rd ed. - Goldstein, Poole & Safko
  • Classical dynamics: a contemporary approach - Jorge V. José, Eugene J. Saletan
  • Classical Mechanics - Systems of Particles and Hamiltonian Dynamics - W. Greiner
  • Mathematical Methods of Classical Mechanics, 2nd ed. - V.I. Arnold
  • Mechanics 3rd ed. - L. Landau, E. Lifshitz

Statistical Mechanics:

  • L. E. Reichl: A Modern Course in Statistical Physics, 2nd ed.
  • R. K. Pathria: Statistical Mechanics
  • M. Plischke & B. Bergesen: Equilibrium Statistical Physics
  • L. D. Landau & E. M. Lifshitz: Statistical Physics, Part 1
  • S.-K. Ma, Statistical Mechanics, World Scientific

Quantum Mechanics:

  • Quantum Mechanics - an Introduction, 4th ed. - W. Greiner
  • R. Shankar, Principles of Quantum Mechanics, Plenum
  • Quantum Mechanics - Symmetries 2nd ed. - W. Greiner, B. Muller
  • Quantum Mechanics - Vol 1&2 - Cohen-TannoudjiJ.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley

Electrodynamics:

  • J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons.
  • Electromagnetic Fields And Waves - lorrain and corson
  • Classical Electrodynamics - W. Greiner
  • Introduction to Electrodynamics - D. Griffiths
  • Quantum Electrodynamics - 3rd ed., - W. Greiner, J. Reinhardt

Optics:

  • Principles of Optics - M.Born, E. Wolf
  • Principles Of Nonlinear Optics - Y. R. Shen

Thermodynamics:

  • Thermodynamics and an Introduction to Thermostatistics 2ed - H. Callen
  • Thermodynamics and statistical mechanics - Greiner, Neise, Stoecker

Solid State Physics:

  • Solid State Physics - Ashcroft, Neil W, Mermin, David N
  • Introduction to Solid State Physics 7th edition- Kittel, Charles

Special Relativity:

  • Classical Mechanics - Point Particles And Relativity - W. Greiner
  • Introduction to the theory of relativity and the principles of modern physics - H. Yilmaz

General Relativity:

  • J.B. Hartle, Gravity, An Introduction to Einstein’s General Relativity, Addison Wesley, 2003.
  • T.-P. Cheng, Relativity, Gravitation and Cosmology, A Basic Introduction, Oxford Univ. Press, 2005.

Particle Physics:

  • Introduction to Elementary Particles - D. Griffiths
  • Fundamentals in Nuclear Physics - From Nuclear Structure to Cosmology - Basdevant, Rich, Spiro

Field Theory:

  • B. de Wit & J. Smith, Field Theory in Particle Physics, North-Holland
  • C. Itzykson & J.-B. Zuber, Quantum Field Theory, McGraw-Hill.

String Theory:

  • Barton Zwiebach, A First Course in String Theory, Cambridge Univ. Press, 2004
  • M.B. Green, J.H. Schwarz & E. Witten, Superstring theory, Vols. I & II, Cambridge Univ. Press

Cosmology:

  • An Introduction to cosmology, 3rd Ed – Roos
  • Relativity, thermodynamics, and cosmology - Tolman R.C.

General:

  • J.B. Marion & W.F. Hornyak, Principles of Physics, Saunders College Publishing, 1984, ISBN 0-03-049481-8
  • H. Margenau and G.M. Murphy, The Mathematics of Physics and Chemistry, D. v.Nostrand Comp.
  • R. Baker, Linear Algebra, Rinton Press

Find lists of other useful textbooks here: Mathematics, Physics (most of these are rather for amusement than being essential for understanding the World), or a little bit more seriously: Physics.

26 Responses and Questions

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More information

  • Chinese version see here
  • Original version see here