BenTheMan

I don't know---it'll give him (her?) something to look forward to. Even when you're teaching students, it always makes sense to keep them focused on where they want to get. Maybe somerlad buys a QFT book an reads the introduction, and gets an idea of what kinds of things are important to focus on, if this is what he's interested in. For example, if you're interested in high energy theory, I would focus much attention on Classical Dynamics (usually the first semester of a two semester course in undergrad), electrodynamics, and quantum mechanics. If you are interested in condensed matter physics, you want to understand statistical mechanics, electrodynamics and quantum mechanics. If you are interested in astrophysics, then you want to understand classical dynamics very well, etc. etc. Even if (s)he's interested in the whole of physics, it's a good idea to keep in mind the canonical textbooks. But, of course, this is just my opinion.

Also, I wrote this about the mass of a photon. You can do some back of the envelope type calculations to see how incredibly small it has to be. http://www.sciforums.com/showpost.php?p=1391396&postcount=48 PS: Maybe this forum doesn't have the same problem, but SciForums seems to be polluted with crackpots. Be careful of what you believe.

I wrote something on another forum about the higgs, here: http://www.sciforums.com/showthread.php?t=68189 It was subsequently attacked by crackpots. Ekpyrotic--- Plus, if the photon were massive, it would make EM a short range force, with a range proportional to the Compton wavelength of the photon.

This is the same as asking ``Why is gravity weaker than electromagnetism?'', or, more directly ``Why is an electron's mass 511 keV?''. There may not even BE an answer. This is more of a philosophical question, in some sense. Suppose that there are an infinite string of universes (like the Ekpyrotic scenario, which I think you are familiar). Now, suppose each time a universe is created, the coupling constants and such are random values. Well, with an infinite string of universes, it should be no surprise to find values SOMEwhere that are similar to the values of things like masses that we observe here in our universe. This is bordering on something called the anthropic principle. One can note that, without very specific values for fundamental constants in our universe, intelligent life would be impossible. (For example, if the cosmological constant were not small and positive, then the universe would expand too quickly for life to evolve, or it would collapse back on itself.) But because there is intelligent life, the fundamental constants have to be exactly as they are. It is a circular argument, to be sure. And some people really hate it. I'm not such a huge fan myself. Either way, you can either accept the anthropic principle, or accept the fact that there is some deeper theory which predicts things like masses of top quarks, like string theory.

No one said it would be easy:)

Yeah Ekpyrotic--- Depending on how technical you want to get, a mass term in the lagrangian is an interraction between two fields and a dimensionful coupling constant. So mass IS an interraction (you're right about that). But we can also have an interraction between three fields or four fields, with a coupling constant that is dimensionless (i.e. has no units if hbar = c = 1). In fact, when everything is massless, the mass terms for fermions are interractions between two fermions and a higgs, with a dimensionless coupling constant. It is only when the higgs gains a vev that the effective coupling constant becomes dimensionful, and the terms become mass terms.

If you can get this page to load (I couldn't), this gives you some directions from one of the greatest physicsts of our times: http://www.phys.uu.nl/~thooft/theorist.html

Jim---do you have a QFT book? Any good book on quantum field theory will help you with this question. A free one is available by Mark Srednicki: http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Also check out Peskin and Schroeder, which is pretty much the standard now. Weinberg's book is pretty uncomprehensible unless you are Weinberg. Other good books are by Ryder, and Itzykson and Zuber. The IZ textbook I saw in Barnes and Noble for $40 the other day, which is a steal. For a more pedagogical approach, try Tony Zee's ``QFT in a Nutshell''.

Ekpyrotic--- This is a question I had once. Here's how I finally got back to sleeping at night:) The thing is, the top quark is fundamental (as you pointed out), so---if you don't believe string theory---zero dimensional! But what is mass, really? In high energy physics, mass is just some arbitrary parameter---the mass comes from the coupling of the particle to the higgs field. So, whereas a gold neucleus is made up of a bunch of up and down quarks which couple very weakly to the higgs field, the top quark couples very strongly to the higgs field. Think of it like this---suppose you have two (metal) blocks and a huge magnet. Now you know that some materials are attracted more strongly to a magnet, so you wouldn't be surprised if you found that one of the blocks was very easy to move around in the magnetic field, and one of the blocks were very difficult to move around in the magnetic field. You would think ``Oh, well, one of these blocks just has a bigger magnetizaion''. The same is true for the top quark and the up/down quarks. The top quark couples more strongly to the higgs field. Hope this helps.

Jim--- I think the error is here: The Lie Algebras have special properties which govern what types of representations you're allowed to use. For example, for [math]U \in SO(N)[/math], we know [math]U^TU = \mathbb I [/math], where [math]\mathbb{I}[/math] is the identity. The matrices which live in the group [math]GL(N,\mathbb{R})[/math] don't obey the same properties. The group SO(3,1) consists of special (S) orthogonal (O) matrices. Special means determinant one, and orthogonal means [math]U^TU = \mathbb I [/math]. The GL consist of general(G) Linear (L) matrices. Linear in the sense that one can solve linear equations (i.e. the matrices are invertible and don't have a zero determinant) and general in the sense that anything goes. So, I think that one can't find unitary representations of the GL group. I DO think that there is an embedding of SO(N) in [math]GL(N,\mathbb{R})[/math]. That is, I think you may be able to find a subset of general linear matrices which obey the SO(N) algebra. Check out this: http://en.wikipedia.org/wiki/General_linear_group. I am wrong a lot, though, especially when it comes to math, so if anyone else has a better answer please don't hesitate to point this out to me.