Bundles, Connections and Gauge theories.

Last week I began a course on particle physics, focused on the electroweak interactions. By a first time I understood how the SU(2)xU(1) symmetry works.

Moreover, this draw a mental picture of how the mathematical concepts of principal bundle and connections are realized on a gauge theory.

If you are looking for a mathematical explanation, there are thousand of books, but some of my favorites are:

1. Choquet-Bruhat, Y. et al. Analysis, Manifolds and Physics. A set of two volumes containing the most useful concepts for Mathematical-Physics... including many applications.
2. Nakahara. Geometry, Topology and Physics.
3. Sen and Nash...
4. Quantum Fields and Strings. A course for mathematicians. A set of two books containing a one-year programme from the IAS

For the physical explanation, the availability of literature is even wider then the above. I study from time to time based on

• P. Ramond. Field Theory. A modern prime.
• Peskin and Schroeder.
• Mandl and Shaw.

but, a complete book is the set of

• S.Weinberg, The quantum Theory of Fields.

And finally one of my personal heroes,

• H. Georgi. Weak Interaction.

this author has a book called ``Lie Algebras in Particle Physics'', both of them are amazing.

On future post I expect to have a change of explaining my personal point of view.

Oscar.

New Semester

Well, after no vacations, I've returned to studying... this new semester brings much more expectatives than I could ever imagine.

I'm taking 3 courses (my last ones)

1. Particle Physics II: It begins with the electroweak interactions of particles and ends with GUTs and SUSY theories.
2. Quantum Mechanics II: This is great, it to review all QM but using the path integral formalism, then it becomes QFT... and even better, at the end I'm expecting to do some research.
3. Laboratory: Even if I'm not experimentalist, I know it's important, ... the funny thing is that my experiment is to find the terminal velocity of a magneto falling throught a tube.

My professors are Claudio Dib, Ivan Schmidt and Valdes. May I say that Schmidt is one of the guys that compute the cross section for finding the anti-hydrogen atom.

Wait, it's not all... by first time I'll be teacher assistant for a graduate course, Classical Mechanics.

Physics Forums

Like three days ago I found a web page called Physics Forum, It's great... you can post your questions and doubts and people (if they consider it useful) can help you...

I'm posting under the nick name Dox.

Enjoy it.

Classical Mechanics

In spite of the qualifying exam in reviewing classical mechanics' topics, this time the book I'm using is Mathematical Methods of Classical Mechanics by V. I. Arnold.

What a great book... despite the author is a mathematician, he gives the physical intuition and lots of examples. Furthermore, the selection of problem goes from very basics up to ``almost impossible" ones.

The second chapter (on the equations of motion), begins with an introduction of stability of differential equations and flows, et cetera. and ends with the method of similarity... section with is even better than the equivalent section on Landau-Lifschitz's book. The final section of the fifth chapter describes parametric oscillations. Similarly, the sixth chapter bring a detailed treatment of the rigid bodies mechanics. And so on. Try it, you'll love it.

Constraints on physics.

I'm beginning to study constraint systems in physics.

Some references are

1. Lectures on Quantum Mechanics by P. A. M. Dirac
2. Quantization of gauge systems by M. Henneaux and C. Teitelboim.
3. Regge, Teitelboim
4. Hamilton's formalism for systems with constraints by Andreas Wipf
5. Quantization of field with constraints by D. M. Gitman and I. V. Tyutin.

For a mathematical approach,

• Presymplectic Lagrangian Systems. By Mark J. Gotay and Jamen M. Nester.

STATISTICAL PHYSICS

In physics, this subject has been, among others, a nightmare.

Finally, I'm studying seriously both, thermodynamics and statistical mechanics. One of the references I'm using is Statistical Mechanics by Kerson Huang. If I get some free time I'll upload the solutions of several problems on the subject.

Another references:

1. Statistical and Thermal Physics by Reif
   
2. Statistical Physics by Reif
   
3. Thermodynamics By Kubo
   
4. Statistical Mechanics by Kubo.
   

Rainbow Gravity

Last week I wonder because on an article Rainbow Gravity by Joao Magueijo and Lee Smolin.

On the paper they propose that any test particle with energy E see, in fact, a different space time. That's why it's called "Rainbow"... Moreover, due to this, as energy change, the geometry of the spacetime runs just like in the renormalization group.

It could by interesting to study this ideas more precisely... specially for getting the real group evolved on these theories (Doubly Special Relativity and Rainbow Gravity).