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  1. N

    A Decomposition of tensors into irreps (Georgi's book)

    Hello. I just came across this post. I understand how the 2nd term in (4) is to equivalent to the 1st term in the 1st equation i.e. uivjk - ujvik = εijlεlmnunvmk = (δimδjn - δjnδim)umvnk but I am having a mental block regarding how the first term in (4) is equivalent to the 2nd term in the...
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    A Dimensional Regularization of Feynman Integrals

    Thanks again. I think C.14 and C.15 in the Appendix are basically what I was looking for. C.15 would seem to correspond to Peskin's A.51. My intention here was to justify the form of each equation rather that replicate the exact proofs. I think the expansion of Γ(∈) and Γ(∈ - 1) were the...
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    A Dimensional Regularization of Feynman Integrals

    Thanks. There's a lot of heavy math in there but I think I got the main idea. It seems that the following 3 expansions are critical to the derivations. To first order, omitting factors of π etc and putting Δ = m2: a. Γ(ε) = 1/ε - γ b. Γ(ε - 1) = -1/ε + γ - 1 (from WolframAlpha) c...
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    A Dimensional Regularization of Feynman Integrals

    I am looking at Appendix A Equation 52 (Loop Integrals and Dimensional Regularization) in Peskin and Schroeder's book. ∫ddk/(2π)d1/(k2 - Δ)2 = Γ(2-d/2)/(4π)2(1/Δ)2-d/2 = (1/4π)2(2/ε - logΔ - γ + log4π) Can somebody explain how this equation is derived? I would also like to know what the...
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    I Bases for SU(3) Adjoint representation

    I thank you for your patience in answering my questions. My background is in semiconductor physics so this group theory stuff is a little to abstract for me. I think at this point an actual computation would help me immensely. My basic challenge is that in the adjoint representation of SU(2)...
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    I Bases for SU(3) Adjoint representation

    Thanks for your reply. I'm no mathematician so your explanation is a little over my head. So the G-M is one possible basis for SU(3) and the Pauli matrices are the basis of SU(2). Given this I have another question concerning the statement adj(X)Y = [X,Y]. For SU(2) the adjoint generators...
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    I Bases for SU(3) Adjoint representation

    I thought the raising and lowering operators may be involved since they are the eigenstates corresponding to the roots. My hang up is that adj(x)(y) = [x,y] where x,y are 4 x 4 matrices but adj(x) is 8 x 8 which doesn't seem to work. New to group theory ... sorry!
  8. N

    I Bases for SU(3) Adjoint representation

    What are the bases for the adjoint representation for SU(3)?
  9. N

    Running Coupling for Weak Interaction

    Thank you for your response. Yes that makes sense. The thing that confused was the single value quoted in http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple.html#c4. I assume this must refer to some experimentally determined value. I found this post...
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    Running Coupling for Weak Interaction

    How can I derive the running coupling for the weak interaction. I have found derivations for QED and QCD that involve the β function http://www.physics.umd.edu/courses/Phys741/xji/chapter1.pdf but I can't find anything specific for the WI. Thanks.
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    Gluon mass ... yes or no?

    http://physics.stackexchange.com/questions/102011/what-is-the-difference-between-a-charged-rho-meson-and-a-charged-pion page 40 in following http://www.physics.umd.edu/courses/Phys741/xji/chapter3.pdf
  12. N

    Gluon mass ... yes or no?

    OK. I have done a lot more reading about this since my last post and realize that we are really talking about 2 different mechanisms here: Spontaneous chiral symmetry breaking and explicit chiral symmetry breaking. Both have to happen to get mass. My interpretation is that the quark...
  13. N

    Gluon mass ... yes or no?

    Are we talking about a similar mechanism to the way the W and Zs get their mass with the em field explicitly breaking the symmetry? The Goldstone bosons get 'eaten' to form 3 massive pions. Does the rho get its mass in the same way with the different spin accounting for the mass difference...
  14. N

    Gluon mass ... yes or no?

    Not sure I want to go there unless it can be put into much simpler terms.
  15. N

    Gluon mass ... yes or no?

    So I should accept the fact that the gluon may be massless. However, outside of a nucleon I could get a pion (residual strong force) which does have a mass. I assume, this does get its mass from the Higgs.
  16. N

    Gluon mass ... yes or no?

    I know gauge theory predicts gluons are massless. But under spontaneous symmetry breaking do they get a mass? If they are massless why is the strong force such short range? Is it because of quark confinement and asymptotic freedom? It seems like a paradox.
  17. N

    Color Singlets Formation

    yes, I understand the formation of the color singlet from 3 x 3 x 3 = 1 + 8. What I don't understand is how you create a proton wavefunction that embodies spin 1/2, isospin 1/2 and is colorless. In the Wikipedia article, the wf is the product of 3 matrices. To create a colorless photon do...
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    Color Singlets Formation

    I am trying to conceptually understand how form a color singlet for baryons and mesons. For example, the Wikipedia article http://en.wikipedia.org/wiki/Isospin shows how to construct the proton and neutron states in terms of isospin and spin. How does one create a color singlet corresponding...
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    W Boson Energy (Mass)

    OK. I think I got it. Thanks for you help and patience.
  20. N

    Noether's Theorem and SU(2)

    Certainly not taken the wrong way. I have no background in particle physics. I am a retired electrical engineer with a decent background in QM. I am trying to learn this stuff from books and videos (notably Susskind's videos on the Standard Model). There are lot of gaps that I am trying to...
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    Noether's Theorem and SU(2)

    Maybe I asked the question in the wrong way (or maybe not!). It is possible to use Noether's theorem to show that U(1) symmetry is associated with charge (weak hypercharge). So how do you demonstrate mathematically that SU(2) is associated with weak isospin?
  22. N

    W Boson Energy (Mass)

    OK, I think I am getting more confused. The Higgs gives mass to a real W correct? The virtual W has less mass and mediates the down to up quark transition. It has some mass. Where does that mass come from? Apologies in advance for my lack of understanding. I am a QM guy from years ago!
  23. N

    W Boson Energy (Mass)

    OK, so the Higgs mechanism actually generates the mass and the Uncertainty Principle approach is not quite true but gives some insight as to what is going on. So in the case of neutron to proton decay, where a down quark switches to up and emits a W-, what actually happens at the vertex? The...
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    W Boson Energy (Mass)

    From Leonard Susskind's Standard Model video lecture 6 https://www.youtube.com/watch?v=5rytN74EOi0 minute 44.
  25. N

    W Boson Energy (Mass)

    I have read that W boson get their energy (mass) by temporarily breaking the energy conservation laws in accordance with the Uncertainty principle. I have also read that the W bosons get their mass through the Higgs mechanism. How are these two things reconciled? Is this the distinction...
  26. N

    Noether's Theorem and SU(2)

    Is it possible to prove that weak isospin associated with SU(2) is conserved using Noether's theorem?
  27. N

    Charge of the W bosons in the Higgs Mechanism

    OK. This might be an iterative process for me. Are you saying SU(2)U(1)γ -> U(1)em but there is a subgroup of U(1)em that is still has unbroken symmetry (the photon field)? But I still don't get where the charges for the W0, W1, W2 boson comes from. In the case of fermions, the Higgs field...
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    Charge of the W bosons in the Higgs Mechanism

    I am confused about how the gauge boson W+ and W- get their charge under spontaneous symmetry breaking in the Higgs mechanism. Here's what I have so far: The covariant derivative for a SU(2)⊗U(1) is DμΦ = (∂μ + igWμiσi/2 + ig'Bμ)Φ where g and g' are coupling constants. SU(2) is associated...
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