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arivero
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How is it that the Coleman Mandula theorem does not tell anything about the values of CKM matrix?
arivero said:How is it that the Coleman Mandula theorem does not tell anything about the values of CKM matrix?
arivero said:How is it that the Coleman Mandula theorem does not tell anything about the values of CKM matrix?
blechman said:Why would it?! CM Theorem is about what kinds of symmetries are allowed in "healthy" quantum field theories. CKM parameters are free parameters of the standard model. What does one have to do with the other?
tom.stoer said:I was never aware of the fact that flavour symmetry becomes a gauge symmetry in these models. Would that mean that you have flavor gauge bosons?
tom.stoer said:I was never aware of the fact that flavour symmetry becomes a gauge symmetry in these models. Would that mean that you have flavor gauge bosons?
arivero said:I do not know how mainstream they are, but if a GUT multiplet includes particles with different generations, it means that you have flavour-changing currents. So perhaps the horizontal "flavour" symmetry of such models is a different beast, or perhaps it is another way to bypass Coleman Mandula. The "small print" of CM mumbles something about "non trivial scattering".
Of course this should aply to Garret's too, but his model already ignores CM in a different way, having both bosons and fermions in the same representations.
tom.stoer said:fancy ...
the main problem is that one can write down the GR, QED and QCD Lagrangians in one line; for the el.-weak theory one needs approx. one page.
I was a member of a group doing non-perturbative canonical quantization of QCD in non-covariant but physical gauges w/o ghosts; therefore I know what lengthy expressions are :-)blechman said:Have you ever written out the GR action by expanding [itex]g=\eta+h[/itex] (what you need to do perturbative calculations in GR)? Or the QCD Lagrangian by expanding out [itex]F_{\mu\nu}^a[/itex]? The latter takes a page, the former takes a forest, and you're still not able to do it!
blechman said:But FCNC's have nothing to do with CM! Almost all extensions of the standard model have FCNC's, none of them violate CM.
blechman said:I suspected that might have been your confusion.
If your argument is correct, then the Standard Model must be wrong! The SM groups the top and bottom quark into the same SU(2) multiplet, and yet they have different masses!
hamster143 said:I concur with blechman (naturally)... Sans Higgs, all fermions are massless (or perhaps have the same mass? - in agreement with Coleman-Mandula), and CKM does not exist because you can always find a basis where it's diagonal. When Higgs is spontaneously broken, fermions acquire nontrivial masses, and CKM acquires nontrivial off-diagonal terms.
My question is: what happens at 200 GeV, which is neither "high" or "low"?
I think there is more to it than what I was saying. In particular: every reference to CM has to do with *SPIN* constraints, not mass constraints. So I am starting to think that we're missing something else...
[Given various assumptions] the most general Lie Algebra of symmetry operators that commute with the S matrix, that take single-particle states into single-particle states, and that act on multiparticle states as the direct sum of their action on single particle states consists of the symmetry generators [itex]P_\mu[/itex] and [itex]J_{\mu\nu}[/itex] of the Poincare group, plus ordinary internal generators that act on one-particle states with matrices that are diagonal in and independent of both momentum and spin.
For example, the "flavor states" (that is: states that are annihilated by the quark operators in the flavor basis)
The Coleman Mandula Theorem is a fundamental result in theoretical physics that states that in a Poincaré invariant quantum field theory, symmetries can only be either space-time symmetries or internal symmetries, but not both. It has important implications for the structure of physical theories and has been a crucial tool in the development of quantum field theory.
The CKM Matrix is a matrix used in the Standard Model of particle physics to describe the mixing of quarks, specifically the up, down, and strange quarks. It is named after physicists Makoto Kobayashi, Toshihide Maskawa, and Nicola Cabibbo, who first proposed its existence in the 1960s.
The Coleman Mandula Theorem and CKM Matrix are related through the theory of symmetries in particle physics. The CKM Matrix is an example of an internal symmetry, while the Coleman Mandula Theorem states that internal symmetries cannot be mixed with space-time symmetries in a quantum field theory. Therefore, the CKM Matrix is an important example of the limitations imposed by the Coleman Mandula Theorem.
The Coleman Mandula Theorem places restrictions on the structure of the CKM Matrix and other similar matrices used in the Standard Model. It implies that these types of matrices cannot involve both space-time and internal symmetries, which has important consequences for the interactions between particles and the properties of the Standard Model.
There are some exceptions to the Coleman Mandula Theorem, such as the supersymmetric extensions of the Standard Model. These theories involve additional space-time symmetries that allow for the mixing of internal and space-time symmetries, which is not possible in the original Coleman Mandula framework. However, these exceptions are still subject to other constraints and limitations imposed by the theorem.