Good point, thanks. However, I am not trying to define a Lie group. I can do that but it's not my intent. I want to condense down to the real minimum of saying why we bother with them and how they can help us. Apparently, this is too minimal.
I'm writing some notes for myself (to read in my rapidly approaching declining years) and I'm wondering if this statement is correct. I"m not sure I am posting this question in the right place.
"Summary: The matrix representations of isometric (distance-preserving) subgroups of the general...
I'm having trouble with Rovelli's new book, partly because the info in it is pretty condensed, but also because his subjects are often very different from those in other books on GR like the one by Schutz. For one thing, he never uses the term "manifold", but talks about frame fields, which seem...
Thanks, but that does not answer my question. Greiner uses 1 quark and 1 antiquark to construct the 10-d SU(3) octet, then uses it for mesons and baryons. Is there a better way of constructing the baryon octet? Preferably without my purchasing yet one more QM book. (I don't have access to a...
The question may be ambiguous but it's really simple. One says that the baryon octet is the D(1,1) representation of SU(3), but then uses the same one for mesons. D(1,1) means one quark and one antiquark, which corresponds perfectly to mesons. But how can it explain baryons?
My information and...
Interesting. Where is the gauge theory in GR? For my limited understanding, that would be thru the use of the covariant derivative with Christoffel symbols as connections. But that hardly looks like a new field to me.
My understanding is at the level of Griffiths's Introduction to quantum mechanics or Robinson's Symmetry and the standard model, i.e., using the phi^4 potential to explain the effects of global and local symmetry breaking, Goldstone and Higgs bosons. These books and others use a potential of...
Thanks for you explanation, vanhees71. In fact, the sign of the mass term is intentionally chosen "wrong" so as to go thru what you explain. You give somewhat more detail, tho, so thanks.
Thanks for the tip about the dagger. I know about the ## F^{\mu \nu}F_{\mu \nu} ## term being a photon, but can it represent two of them? How do we know?
I’m reading Lancaster & Blundell, Quantum field theory for the gifted amateur (even tho I”m only an amateur...) and have a problem with their explanation of symmetry breaking from page 242. They start with this Lagrangian:
##
\mathcal{L} =
(\partial_{\mu} \psi^{\dagger} - iq...
In classical mechanics, we have either Newton’s laws or a Lagrangian in terms of coordinates and their derivatives (or momenta) and we can solve them for the behavior of the system in terms of these variables, which are what we observe (measure).
In QM, we quantize classical mechanics by making...
Your equations look good to me. (I envy you. When I did grad work in <1965, there was no course offered in group theory, which is why I'm struggling some now.) Interesting that I have never seen in any of these books what you just went thru. So it all is U(1), it just looks different in the two...
Sorry, I meant Dirac, not K-G. As for the bar, I think it is there, it's just hard to see on the capital ##\Psi ##. At least, I meant to put it there. And, yes, I should have used the same ##\Psi## everywhere.
I guess my first question might have been posed differently. If transformation by...
I am trying to get a foothold on QFT using several books (Lancaster & Blundell, Klauber, Schwichtenberg, Jeevanjee), but sometimes have trouble seeing the forest for all the trees. My problem concerns the equation of QED in the form
$$
\mathcal{L}_{Dirac+Proca+int} =
\bar{\Psi} ( i \gamma_{\mu}...
In his book, "The greatest story ever told", Lawrence Krauss states: "Gauge invariance .... completely determines the nature of electromagnetism."
My question is simple: How?
I have gone back thru the math. Gauge invariance allows us to use the Lorenz gauge with the vector and scalar...
Agreed. That makes four ways of looking at entropy: Q/T of Carnot or Clausius or whoever it was, kln(W) of Boltzmann, disorder (same thing, really), and negative (?) information. Can all these be tied together somehow?
Personally, I don't get the information business, basically because I don't...
One generally speaks of two sets of distinguishable molecules (say, rad and green ones) separated by a membrane. One removes the membrane, they get all mixed up, and the result is more disordered than when they were separated.
What about the case where the red molecules are oxygen and the green...
Sure. I've read textbooks. Just reading this to see how they explain it simply to laymen. Simply does not necessarily equal correctly.
Also, they talk a lot about galaxy formation, about which I know very little. It appears all those (again) simple explanations of just gravity pulling dust...
For those of you who are (quite logically) worrying I have misquoted the book, here is the whole paragraph. It follows an example of time dilation, which terminates and then goes on as follows:
"... In other words, while I may observe ten seconds elapsing, you, who are accelerating away from...
This sounds right, intuitively. It's the case of the pole jumper, for instance. But I can't quite see it mathematically (or on a light-cone diagram).
Thanks, all, for the helpful comments.
So in any case, there is no caused effect here and what the authors of "Bang!" say is ... not wrong. And the order of the two events differs between the two observers.
I'm reading "Bang!", by Brian May, Patrick Moore and Chris Lintott. On page 40, they say:
"So one [observer] may believe A preceded B by a minute, and another that A and B were simultaneous, it is impossible for any observer to see B preceding A. Hence cause and effect are preserved..."
But in...
There is a great deal of discussion of information in the context of black holes and whether it is destroyed when it passes the event horizon. Whole books have been written about this, but some folks still claim the problem is not resolved. How is this information defined? It seems to be that...