HOW to BECOME a GOOD THEORETICAL PHYSICIST
by Gerard 't Hooft
This is a web site (still under construction) for young students - and anyone else - who are (like me) thrilled by the challenges posed by real science, and who are - like me - determined to use their brains to discover new things about the physical world that we are living in. In short, it is for all those who decided to study theoretical physics, in their own time.
Note that this site NOT meant to be very pedagogical. I avoid texts with lots of colorful but distracting pictures from authors who try hard to be funny. Also, the subjects included are somewhat focused towards my own interests.
The .ps files are PostScript files §.
(In this initial phase this page is still incomplete!)
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. Now, here begins the serious stuff. Don't complain that it looks like being a lot. You won't get your Nobel Prize for free, and remember, all of this together takes our students at least 5 years of intense study (at least one reader was surprised at this statement, saying that (s)he would never master this in 5 years; indeed, I am addressing people who plan to spend most of their time to this study). More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers. It is necessary to do exercises. Some of the texts come with exercises. Do them, or better, invent your own exercises. Try to outsmart the authors, but please refrain from mailing to me your alternative theories until you have studied the entire lot; if you do this well you will discover that many of these authors were not so stupid after all.
Now, first things first :
Algebraic equations. Approximation techniques. Series expansions: the Taylor series. Solving equations with complex numbers. Trigonometry: sin(2x)=2sin 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
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.
Even the pure sang theorist may be interested in some aspects of Computational physics.
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.
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.
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.
Just to name a few:
Solid State Physics:
Find lists of other useful textbooks here:
Physics (most of these are rather for amusement than being essential for
understanding the World),
or a little bit more seriously: Physics.
There already is some response. I thank: Rob van Linden, Robert Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin, David Cuthbertson, Trent Strong, and many others.
"...You sketch the path for potential students through the forest of college level physics... Two years ago I decided to self-study theoretical physics by following the syllabus of a renown university and the advice from your page and now I'm half-way through the journey but I was wondering about what happens next? Quoting you from the former page "In short, it is for all those who decided to study theoretical physics, in their own time.", Do you know of anyone who got tenure at a physics department or any research institute based on studies he did in his own time without holding a university degree?"
This is not so easy to answer, unfortunately. What I can say, is:
Eventually, whether you like it or not, you will have to obtain some University degree, if you wish a self-supporting career in theoretical Physics. One possibility is to follow a Master course such as the one offered by our University. I don't know about your qualifications, but I suspect that, with enough determination, you may be able to comply.
This is not a burocratic argument but a very practical one. It is also advisable not to wait until you think your self-study is completed. You must allow your abilities to be tested, so that you get the recognition that you may well deserve. Also, I frequently meet people who get stuck at some point. Only by intense interactions with teachers and peers one can help oneself across such barriers. I have not yet met anyone who could do the entire study all by him/herself without any guidance. If you really think you have reached a professional level in your studies, you can try to get admitted to schools, conferences and workshops in topics of your interest.
3/04/06: Message received from John Glasscock, Bloomington, IN:
The only one I know of currently is John Moffatt at U Toronto, who was a student of Abdus Salam at Imperial College, London. He started life as a painter in Paris, had no undergraduate degree, taught himself, corresponded with Einstein, and was admitted, based on his demonstrated original work, at IC. (Source: Joăo Magueijo, _Faster than the Speed of Light_. Perseus Publishing, Cambridge, MA. 2003.)
Suggestions for further lecture notes from Alvaro Véliz:
I thank Aldemar Torres Valderrama for his assistance in updating and renewing numerous links on this page.§ Note that .ps files are PostScript files, so defend yourself against Microsoft PaintShop, that often wants to appropriate .ps files. PostScript files are read using GhostView (gsview) Back to homepage. Your visitor number is: (since 21/8/03)