by Gerard 't Hooft


Note:  This web site will soon be removed from its present address. An updated and renewed version is available at:


This is a web site  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.

It so often happens that I receive mail - well-intended but totally useless - by amateur physicists who believe to have solved the world. They believe this, only because they understand totally nothing about the real way problems are solved in Modern Physics. If you really want to contribute to our theoretical understanding of physical laws - and it is an exciting experience if you succeed! - there are many things you need to know. First of all, be serious about it. All necessary science courses are taught at Universities, so, naturally, the first thing you should do is have yourself admitted at a University and absorb everything you can. But what if you are still young, at School, and before being admitted at a University, you have to endure the childish anecdotes that they call science there? What if you are older, and you are not at all looking forward to join those noisy crowds of young students ?

It should be possible, these days, to collect all knowledge you need from the internet. Problem then is, there is so much junk on the internet. Is it possible to weed out those very rare pages that may really be of use? I know exactly what should be taught to the beginning student. The names and topics of the absolutely necessary lecture courses are easy to list, and this is what I have done below. It is my intention to search on the web where the really useful papers and books are, preferably downloadable as well. This way, the costs of becoming a theoretical physicist should not exceed much the price of a computer with internet connection, a printer, and lots of paper and pens. Unfortunately, I still have to recommend to buy text books as well, but it is harder to advise you here; perhaps in a future site. Let's first limit ourselves to the absolute minimum. The subjects listed below must be studied. Any omission will be punished: failure. Do get me right: you don't have to believe anything you read on faith - check it. Try alternative approaches, as many as you can. You will discover, time and again, that really what those guys did indeed was the smartest thing possible. Amazing. the best of the texts come with exercises. Do them. find out that you can understand everything. Try to reach the stage that you discover the numerous misprints, tiny mistakes as well as more important errors, and imagine how you would write those texts in a smarter way.

I can tell you of my own experiences. I had the extreme luck of having excellent teachers around me. That helps one from running astray. It helped me all the way to earn a Nobel Prize. But I didn't have internet. I am going to try to be your teacher. It is a formidable task. I am asking students, colleagues, teachers to help me improve this site. It is presently set up only for those who wish to become theoretical physicists, not just ordinary ones, but the very best, those who are fully determined to earn their own Nobel Prize. If you are more modest than that, well, finish those lousy schools first and follow the regular routes provided by educators and specialized -gogues who are so damn carefully chewing all those tiny portions before feeding them to you. This is a site for ambitious people. I am sure that anyone can do this, if one is gifted with a certain amount of intelligence, interest and determination.

Theoretical Physics is like a sky scraper. It has solid foundations in elementary mathematics and notions of classical (pre-20th century) physics. Don't think that pre-20th century physics is "irrelevant" since now we have so much more. In those days, the solid foundations were laid of the knowledge that we enjoy now. Don't try to construct your sky scraper without first reconstructing these foundations yourself. The first few floors of our skyscraper consist of advanced mathematical formalisms that turn the Classical Physics theories into beauties of their own. They are needed if you want to go higher than that. So, next come many of the other subjects listed below. Finally, if you are mad enough that you want to solve those tremendously perplexing problems of reconciling gravitational physics with the quantum world, you end up studying general relativity, superstring theory, M-theory, Calabi-Yau compactification and so on. That's presently the top of the sky scraper. There are other peaks such as Bose-Einstein condensation, fractional Hall effect, and more. Also good for Nobel Prizes, as the past years have shown. A warning is called for: even if you are extremely smart, you are still likely to get stuck somewhere. Surf the net yourself. Find more. Tell me about what you found. If this site has been of any help to someone while preparing for a University study, if this has motivated someone, helped someone along the way, and smoothened his or her path towards science, then I call this site successful. Please let me know. Here is the list.

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.


LIST OF SUBJECTS, IN LOGICAL ORDER (not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others).


More resources

The .ps files are PostScript files §.

(In this initial phase this page is still incomplete!)

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. 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.

Return to List

Now, first things first :

Primary Mathematics:
Are you comfortable with numbers, adding, subtracting, square roots, etc.?


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)=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 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.

Return to List

Classical Mechanics:

Return to List


Return to List

Statistical Mechanics and Thermodynamics:

Return to List

(Only some very basic things about electronic circuits)

Return to List

Electromagnetism: Maxwell's Theory for electromagnetism
Maxwell's laws in a medium. Boundaries. Solving the equations in:
The vector potential and gauge invariance (extremely important)
emission and absorption on EM waves (antenna)
light scattering against objects.

Return to List

Computational Physics :

Even the pure sang theorist may be interested in some aspects of Computational physics.




Return to List

Quantum Mechanics (Non-relativistic):

Return to List

Atoms and Molecules:

Return to List

Solid State Physics:

Return to List

Nuclear Physics

Return to List


Plasma physics:

Return to List

Advanced Mathematics:

Return to List

Special Relativity

Return to List

Advanced Quantum Mechanics:

Return to List


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.

Return to List

General Relativity:

Return to List

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.

Return to List

Superstring Theory:

Return to List


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:

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.

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.

Mr. Hisham Kotry came with an important question:

"...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:

1. The archimedeans webpage: It has a lot of lecture notes in Physics and Mathematics from Part I and II from Cambridge.
2. David Tong's (DAMTP)  lectures in classical mechanics I found these lectures fascinating.
3. Bo Thide's (Uppsala) lectures in electromagnetic theory.
4.  Angel Uranga's lectures in String Theory._
5. I found also extremely helpful MIT's OpenCourseWare: Lewin's lectures in basic Physics are terrific (in video).
6. Michael Fowler's (Virginia) lectures in Quantum Mechanics
        (not checked, G. 't H.)

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)
Last revised: 2009
Design by CJ