Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why gauge bosons, but no gauge fermions

  1. May 2, 2005 #1
    Hello all,

    from Marlon's journal, I read the question "DO YOU KNOW WHY FORCE CARRIERS ARE ALWAYS BOSONS ??? WHY DON'T WE HAVE GAUGE FERMIONS ???"

    Can anyone answer this question? :redface:
     
  2. jcsd
  3. May 2, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Give me an example of a fermionic first class system,field theory,of course...

    Daniel.
     
  4. May 2, 2005 #3

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Gauge invariance involves correcting problems caused in quantum mechanics by the appearance of the partial derivatives with respect ot x,y,z,t. These partials form a relativistic 4-vector. This requires 4-vector fields so that (in EM)
    d/dx-->d/dx-ieA_x, etc. The particle excitations of vector fields have spin one.
    So the requirement that gauge particles (the excitations of the gauge fields) must be vector particles follows from the fact that space-time is 4 dimensional.
     
  5. May 2, 2005 #4
    I thought that because the exchange particles must be able to carry integer spin they must be bosons. (Spin flips and all).
    Josh
     
  6. May 3, 2005 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Why would they have to carry integer spin...?

    Daniel.
     
  7. May 3, 2005 #6
    good question...

    there are several ways to answer this : spin statistics being one of them

    marlon :approve:
     
  8. May 3, 2005 #7

    vanesch

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I like that answer :-) As gauge fields have to appear in the covariant derivative, they have to be vector fields. Nice.

    cheers,
    Patrick.
     
  9. May 3, 2005 #8
    In SuperSymmetry, maybe you will call the Fermions in the same doublet with the Bosons "Gauge Fermions", because they transform together with the gauge bosons, for
    example wino or zino (they form chargino and neutrino).
     
  10. May 3, 2005 #9
    This is indeed a great answer

    marlon
     
  11. May 3, 2005 #10
    "Gauge Fermions" in supersymmetry are generically called "gauginos".
    As long as I know, in supersimetric models they contribute with the forces just like regular gauge bosons, but because of the exclusion principle their net effect is not very strong, wich also shows that if we only had "gauge fermions" and no "gauge bosons" the world wouldn't be as we know it at all.
     
    Last edited: May 3, 2005
  12. May 3, 2005 #11

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Unless "vector particle" means something else than the quanta of a vector field,that conclusion is incorrect.

    Daniel.
     
  13. May 3, 2005 #12
    I am not a QFTist and know only a bit of it,so let me ask-----does gravity have to necessarily be a gauge field?If so why?
     
    Last edited: May 3, 2005
  14. May 3, 2005 #13

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Gravity is a gauge field.It's not a vector field (spin 1),but a tensor field (spin 2)...It's the idea behind post #11.

    Daniel.
     
  15. May 3, 2005 #14
    Yeah ok,gravity is a gauge field(only potential differences matter).But some more stupid questions--why does a tensor field have to be spin 2 and vector field spin one?
     
    Last edited: May 3, 2005
  16. May 3, 2005 #15

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Aaa,nice question.:smile:Group theory.Vectors are [itex] \left(\frac{1}{2},\frac{1}{2}\right) [/itex] irreducible reps of the restricted homogenous Lorentz group and therefore have total spin [itex] \frac{1}{2}+\frac{1}{2}=1 [/itex].

    Symmetric 2-nd rank tensors (the gravity field [itex] h_{\mu\nu} [/itex] which is the I-st order perturbation expansion of GR metric [itex] g_{\mu\nu} [/itex]) are [itex] (1,1)\oplus (0,0) [/itex] irredcible reps of the restricted homogenous Lorentz group and have spin [itex] 1+1=2 [/itex].

    Daniel.
     
  17. May 3, 2005 #16
    put it in a language that's more comprehensible
     
  18. May 3, 2005 #17

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I honestly can't."Spin" means group theory.Vectors & tensors mean group theory.That's all there is to it...All u need to understand is the 'coupling' between spin & Lorentz group...

    Daniel.
     
  19. May 3, 2005 #18

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Quantum spin is a new concept. That means it can't really be explained in terms of older concepts. If you don't want to learn the group theory definitions, you can just accept the fact that the states of spin 1/2 only turn half as fast as the coordinates do when you perform a rotation.
     
  20. May 3, 2005 #19

    Haelfix

    User Avatar
    Science Advisor

    Agreed with Dexter.

    Although in Supersymmetry the fundamental axioms of Lie algebra are modified (into.. surprise Super Lie Algebra), which is why you can have 'gauge' fermions with the same standard model quantum numbers, and they do indeed participate. However for technical reasons they have to be Majorana fermions, and when you calculate the beta function you end up with a fraction of the contribution as the gauge boson (tho not too small, maybe an order of magnitude less). Of course super symmetry is badly broken, and depending on the mechanism choice, will reduce things further.
     
  21. May 3, 2005 #20
    SU(2) you mean--i know that.please complete the argument.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?