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QED vs Higgs mechanism

  1. Jul 11, 2012 #1
    I understand that an electron gets its mass by self-interaction of its fields which is explained by QED, but on the other hand there is the higgs mechanism which gives mass to all the fundamental particles.
    Does the electron have two types of mass one which is due to the QED mechanism and the other due to the Higgs mechanism, if so which mass is considered for the gravitational interactions and why??
    I believe that QED is incomplete in the sense that it involves a singularity while calculating the mass, so does the singularity affect in determining the actual mass due to self-interaction??
    Can we apply QED type theory to other charged sub-atomic and fundamental particles, if so, all these particles will have a mass due to self-interaction and also due to higgs mechanism, so this leads to a conclusion that masses are of two types??? Are these masses related, if so the can we conclude QED and Higgs mechanism are related in some manner???
     
    Last edited: Jul 11, 2012
  2. jcsd
  3. Jul 11, 2012 #2
    The singularities of QED are renormalisable, so -as a theory- it's not problematic.

    Now on the electron mass, I think that no, you don't have such... Electron gets part of its mass from the Higgs field (I am 80% sure of this).

    your last question I didn't get...
     
  4. Jul 11, 2012 #3
    I've never heard of this. To my understanding electron self-interaction is unsolved problem, but I'm happy to be proved otherwise.

    Electron is elementary. There are no particles which constitute the electron.

    Yes. The theory of quantum electrodynamics can be applied to muon, tauon and all quarks with little modifications (different masses and charges). As is you cannot use it to describe bosons (like W).
     
  5. Jul 11, 2012 #4

    vanhees71

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    In the standard model the mass of the leptons and the current-quark masses are indeed due to the Higgs mechanism. You have to start with massless matter fields, because the electroweak sector of the standard model is a gauged chiral symmetry, and this symmetry must not be broken explicitly in any way.

    Now the trick with the Higgs mechanism (more justly we should name it Anderson-Higgs-Kibble-Brout-Englert-et-al mechanism ;-)) is that you are free to introduce also boson fields which can couple to the fermion fields in way not to violate thnis local chiral gauge invariance, and you can give these bosons a mass term with the "wrong sign". Together with the self-coupling of these boson fields this leads to spontaneous symmetry breaking, i.e., the state of lowest energy in this boson sector is not for 0 fields but at a finite vacuum expectation value.

    In the minimal version, you introduce a boson doublet in the sense of the underlying SU(2) gauge symmetry. All together you have 2 complex, and this means four real bosonic field-degrees of freedom. Now this symmetry is a local one, and this means that at the end there is only one massive boson left in the particle spectrum, while the other three field-degrees of freedom are absorbed in the gauge bosons of the spontaneously broken SU(2) gauge group. This additional degree of freedom is needed, because in this way these gauge fields become massive, and massive gauge bosons have three physical polarization states and not only two as massless ones have. This was the great discovery by Higgs and many others in 1964, namely that spontaneous symmetry breaking of a local gauge symmetry does not lead to the appearance of massless Goldstone modes as is the case for global symmetries but to the appearance of massive gauge bosons without breaking local (non-Abelian) gauge symmetry explicitly. Later, 't Hooft and Veltman have proven that such models stay also renormalizable as non-broken local non-Abelian gauge models.

    Now, due to the gauge invariant coupling of the leptons and quarks to the Higgs field, also these particles become massive on the spontaneously broken phase as it must be. In addition you also have, what's called mixing: The flavor eigenstates of the leptons and quarks are not identical with the mass eigenstates, but this is only a detail, which is not so important to understand the Higgs mechanism itself.
     
  6. Jul 11, 2012 #5

    I like that explanation coz at a test we were asked about that extra degree of freedom appearing and what it means, and I could not answer the question... So I would like to ask you from where you got that info (book/internet) ? :)
    thanks
     
  7. Jul 11, 2012 #6
    Conclusion being????
     
  8. Jul 11, 2012 #7
    I did not give detailed information regarding the self-interaction or self-energy as it would have made the thread lengthier.
    The problem of self-energy is well known both in classical and quantum physics, lorentz and maxwell tried to solve it using classical theory but were unsuccessful, Dirac tried next and came close to solving it by giving an equation similar to lorentz but in relativistic form known as Lorentz-Dirac equation which was 3rd order rather than 2nd order which led to the problem of initial acceleration to be given or else it would let to infinite number of meaningless physical solutions.
    QED was then used to solve it, but it led to more complications as it gave rise to more divergent integrals including the all the ones describing the self-interactions by perturbation theory.Many scientists attempted mass re-normalization but it is not considered as it is mathematically weak.
    I agree with you partly in the sense that mass has not yet been calculated and there is ambiguity, but the self-interaction is well described by both lorentz-dirac eqation and QED, i had mentioned the structure of an electron as it is involved in some of the mathematical models describing self-energy but it is widely accepted that electron is a point-like particle with no structure.
     
  9. Jul 11, 2012 #8
    Thanks. I was not aware that the renormalization was tied to self interactions.
     
  10. Jul 11, 2012 #9

    arivero

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    All we can say of the self-energy is that we expect to be of the same order that the bare mass. For the electron, this is true if you put the cut-off at Planck scale; in fact you get a pretty equation relating exponentially the max of plank and the electromagnetic mass, with the fine structure constant in the exponent. Some people will even try to sell you this exponential as a prediction of the electron mass (eg "Scale Relativity") but it really is a QED mass renormalisation (see Polchinski vol II)
     
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