How to become a GOOD Theoretical Physicist
Table of Contents
 1 Languages
 2 Primary Mathematics
 3 Classical Mechanics
 4 Optics
 5 Statistical Mechanics and Thermodynamics
 6 Electronics
 7 Electromagnetism
 8 Computational Physics
 9 Quantum Mechanics (Nonrelativistic)
 10 Atoms and Molecules
 11 Solid State Physics
 12 Nuclear Physics
 13 Plasma Physics
 14 Advanced Mathematics
 15 Special Relativity
 16 Advanced Quantum Mechanics
 17 Phenomenology
 18 General Relativity
 19 Cosmology
 20 AstroPhysics and Astronomy
 21 Quantum Field Theory
 22 Supersymmetry and Supergravity
 23 Astro Particle Physics
 24 Super String Theory
 25 Texts and Other resources
 26 Responses and Questions
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 skyscraper, 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 manybody 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 NavierStokes 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 2dimensional 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 (Nonrelativistic)
 Bohr’s atom
 DeBroglie’s relations (Energyfrequency, momentumwave 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 Smatrix. Radioactive 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
 Radioactivity
 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
 \(E = mc^2\)
 4vectors and 4tensors
 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 supraconductivity
 Quantum Hall effect
 Advanced scattering theory
 Dispersion relations
 Perturbation expansion
 WKB approximation, Extremum principle
 BoseEinstein condensation

Superliquid helium
 Prof. Stringari’s course on Ultracold Fluids.
 Introduction to the Quantum Hall effect by A.H. MacDonald
 Introduction to Coherent States and Quantum Information Theory by K. Fujii
 Tutorial on Quantum information by Peter Zoller
 Intoduction to Quantum Computation by A. Chatterjee
 Advanced QM by Freeman J. Dyson
 K. Schulten’s notes on advanced QM
 James Branson, Advanced Quantum Theory
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
 Spacetime curvature
 Einstein’s gravity equation
 The Schwarzschild black hole
 ReissnerNordström 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 AstroPhysics 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, Diracspinor, YangMills vector fields.
 Interactions, perturbation expansion. Spontaneous symmetry breaking, Goldstone mode, Higgs mechanism.
 Particles and fields: Fock space. Antiparticles. Feynman rules. The GellMannLévy sigma model for pions and nuclei. Loop diagrams. Unitarity, Causality and dispersion relations. Renormalization (PauliVillars; dimensional ren.) Quantum gauge theory: Gauge fixing, FaddeevPopov 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. BetheSalpeter 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 nongravitational supersymmetric theories, such as the Minimal Supersymmetric Standard Model). Since the generators of supersymmetry (SUSY) are convoluted with the Poincaré group to form a superPoincaré 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; largescale 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 Mtheory.
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  CohenTannoudjiJ.J. Sakurai, Advanced Quantum Mechanics, AddisonWesley
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, NorthHolland
 C. Itzykson & J.B. Zuber, Quantum Field Theory, McGrawHill.
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 0030494818
 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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