Help with Theoritical Physics self-study program.

[Askalany]

Hi,

I am going to start from Zero in theoretical physics, and have no chance to study it in a university now, so I will do self-study until I can do graduate study in physics, I am an EE so I have background in physics and maths.

so, please I need someone to help me with the following:
- field in maths and physics I should build a strong background in.
- book name (best) in each filed.
- a path to take in such self-study program, which to do first and so on.

thanks.

 

[Etenim]

Hey,

I copied the following (dotted) list of books out of a paper on Loop Quantum Gravity (Thiemann, "Lectures on Loop Quantum Gravity"), because I couldn't write a better one.

• General
A fairly good encyclopedia is
Y. Choquet-Bruhat, C. DeWitt-Morette, “Analysis, Manifolds and Physics”, North Holland,
Amsterdam, 1989 (Volumes 1 and 2)

• General Topology
A nice text, adopting almost no prior knowledge is
J. R. Munkres, “Toplogy: A First Course”, Prentice Hall Inc., Englewood Cliffs (NJ), 1980

• Differential and Algebraic Geometry
A modern exposition of this classical material can be found in
M. Nakahara, “Geometry, Topology and Physics”, Institute of Physics Publishing, Bristol, 1998

• Functional Analysis
The number one, unbeatable and close to complete exposition is
M. Reed, B. Simon, “Methods of Modern Mathematical Physics”, vol. 1 – 4, Academic Press,
New York, 1978
especially volumes one and two.

• Measure Theory
An elementary introduction to measure theory can be found in the beautiful book
W. Rudin, “Real and Complex Analysis”, McGraw-Hill, New York, 1987

• Operator Algebras
Although we do not really make use of C∗−algebras in this review, we hint at the importance
of the subject, so let us include
O. Bratteli, D. W. Robinson, “Operator Algebras and Quantum Statistical Mechanics”, vol.
1,2, Springer Verlag, Berlin, 1997

• Harmonic Analysis on Groups
Although a bit old, it still contains a nice collection of the material around the Peter & Weyl
theorem:
N. J. Vilenkin, “Special Functions and the Theory of Group Representations”, American Mathematical
Society, Providence, Rhode Island, 1968

• Mathematical General Relativity
The two leading texts on this subject are
R. M. Wald, “General Relativity”, The University of Chicago Press, Chicago, 1989
S. Hawking, Ellis, “The Large Scale Structure of Spacetime”, Cambridge University Press,
Cambridge, 1989

• Mathematical and Physical Foundations of Ordinary QFT
The most popular books on axiomatic, algebraic and constructive quantum field theory are
R. F. Streater, A. S. Wightman, “PCT, Spin and Statistics, and all that”, Benjamin, New
York, 1964
R. Haag, “Local Quantum Physics”, 2nd ed., Springer Verlag, Berlin, 1996
J. Glimm, A. Jaffe, “Quantum Physics”, Springer-Verlag, New York, 1987

I, personally, haven't read a single one of those, but they all seem to be very mainstream and widely used. Books I have experience with and can recommend are,

Hrbacek - Introduction to Set Theory
Lang - Underg. Analysis
Sternberg - Advanced Calculus (huge, available online, together with a number of other books which will be of great use to you, see Shlomo Sternberg's faculty page -- Chapters 0 and 1 alone are worth working through)
Rudin - Principles of Mathematical Analysis

Greub - Linear Algebra
Halmos - Finite-dimensional Vector Spaces
Lang - Linear Algebra
Sharipov - Linear Algebra (available online)

Lang - Underg. Algebra
Hungerford - Algebra
MacLane - Algebra
Connell - Elements of Abstract and Linear Algebra (available online)
Rotman - An introduction to the theory of groups

These books are mainstream, too, but still too advanced for me:

Rudin - Functional Analysis
Awodey - Category Theory (does not presuppose much knowledge)

On Mathematical Physics:
Szekeres - A course in modern mathematical physics
Geroch - Mathematical Physics

Other good books are available online by Gerald Teschl (University of Vienna) on ODEs, Dynamical Systems Theory, Functional Analysis, Operator Theory.

Mathematics is essentially non-linear. There is no clear path. You will have to study multiple disciplines of mathematics and physics at the same time. Someone else can enlighten you on this topic, perhaps.

Cheers,
Etenim.

 

[Askalany]

Thanks Etenim, I appreciate your effort. :)

 

[xepma]

I'm sorry to say it, but those books and topics seem hardly relevant for someone who starts from zero in theoretical physics. Most of these books are very advanced already (who needs books on operator algebras or foundations of QFT?) and will just scare someone off the field. This list does not apply for 'basic' general theoretical physics.


Why don't you start off with explaing what exactly your background is. Have you ever been exposed to Quantum Field Theory, perturbation theory in quantum mechanics, electrodynamics or general relativity? What's your background in mathematics? (i.e. does differential geometry, group theory, complex analysis sound familiar to you?)

Taking on the whole field is quite tough on your own (I wouldn't say it is impossible though). Is there any field you would like to specialize in? E.g. theoretical particle physics, string theory, condensed matter theory, etc.

 

[Etenim]

I'm sorry to say it, but those books and topics seem hardly relevant for someone who starts from zero in theoretical physics.

The list is obviously only for the mathematical side of his plan to study theoretical physics, and those topics are essentially relevant. The books I have listed range from almost zero to a very sophisticated level of mathematics.

who needs books on operator algebras or foundations of QFT

All those who are interested. Even if you specialize at some point, a broad knowledge is always useful.

 

[xepma]

Look, ofcourse those books are useful once you start specializing. But as far as I can tell the poster states that he a) starts off from zero and b) enters a graduate program later on. The list you mentioned takes years to work through and hardly covers all relevant aspects of theoretical physics - let alone prepare you for a graduate course. You talk about a broad context, but this list is obviously ment for a specialized audience.

 

[George Jones]

Etenim, you have certainly listed some interesting and good books, but I agree with xepma. While I think abstract mathematics is necessary in certain branches of theoretical physics (see https://www.physicsforums.com/showthread.php?p=1008436#post1008436), I don't think it is necessary in all branches of theoretical physics. Askalany needs first to study the basic core of undergraduate physics. Also, Askalany is doing this on the side and through self-study, which makes things doubly difficult; the topics have to be limited.

Below, I give what I consider to be the (beginnings) of the basic core. I may have missed some important topics, and people may disagree vehemently with some of my choices. I don't think that the set of books for any particular topic is a totally order set, i.e., I don't think there are "best books."

Mathematical Methods:
Mathematical Methods In the Physical Sciences by Mary Boas.

Thermal Physics:
An Introduction to Thermal Physics by Daniel V. Schroeder.

Electromagnetism:
A Student's Guide to Maxwell's Equations by Daniel Fleisch;
Introduction to Electrodynamics by David J. Griffiths.

Special Relativity:
A Traveler's Guide to Spacetime: An Introduction to the Special Theory of Relativity by Thomas A. Moore;
Spacetime Physics by Edwin F. Taylor and John A. Wheeler.

Classical Mechanics:
Analytical Mechanics by Grant R. Fowles and George L. Cassiday ;
Classical Mechanics by John R. Taylor.

Quantum Mechanics:
Quantum Mechanics by David J. Griffiths.

 

[Etenim]

Askalany needs first to study the basic core of undergraduate physics. Also, Askalany is doing this on the side and through self-study, which makes things doubly difficult; the topics have to be limited.

This is certainly true. I apologize for having brought the conversation off topic. :shy:

 

[Askalany]

thanks all, about my background; I have studied Mathematics and Physics in my college, I am familiar with:

- Complex analysis.
- Electromagnetism (Maxwell equations, Tensors).
- Modern Physics (in broad means).
- Differential Equations.
- Calculus (but I can't know how far I am, took theorems like stoke's ...).
- General Relativity.
- I am preparing myself in the Statistics and Probability field.

About specialization in a field inside theoretical physics is far now, I want to have a good knowledge first, then I can decide.

 

[Monocles]

Stoke's theorem is about as far as calculus goes before the line starts blurring between calculus and analysis or differential geometry etc. So you're good in that department.

 

[Askalany]

Thanks all.

 

[Troponin]

My favorite site for Physics self-study

http://www.phys.uu.nl/~thooft/theorist.html

 

[Askalany]

Thanks Troponin for the site.