# Search results

1. ### A Simple definition of Lie group

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...
2. ### A Frame fields

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...
3. ### A Why does D(1,1) representation of SU(3) give baryon octet?

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...
4. ### A Justification for phi^4 potential

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...
5. ### I Gauge theory symmetry breaking in L&B

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...
6. ### I Where do wave functions come from?

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...
7. ### A Symmetry of QED interaction Lagrangian

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}...
8. ### How does gauge invariance determine the nature of electromagnetism?

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...
9. ### B Order of events and cause and effect

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...
10. ### I Understanding parallel transfer

I've read Collier's book on General Relativity and consulted parts of Schutz, Hartle and Carroll. In the terms they use, i have yet to gain anything resembling an intuitive understanding of parallel transport. In fact, it seems to me it is usually presented backwards, saying that the geodesic...
11. ### I Gradient one-form: normal or tangent

Working through Schutz "First course in general relativity" + Carroll, Hartle and Collier, with some help from Wikipedia and older posts on this forum. I am confused about the gradient one-form and whether or not it is normal to a surface. In the words of Wikipedia (gradient): If f is...
12. ### Relativity Error in Hartle's Fig. 7.11?

A question concerning FIg. 7.11 on page 173. It seems to me, in light of what is said on the preceding page about null surfaces, that he has interchanged "normal" and "tangent" in the third and fourth sentences of the figure caption. I would say: "The tangent to the surface l lies in the...
13. ### Units if conversion between covariant/contravariant tensors

I am still at the stage of trying to assimilate contravariant and covariant tensors, so my question probably has a simpler answer than I realize. A covariant tensor is like a gradient, as its units increase when the coordinate units do. A contravariant tensor's components decrease when the...