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Quanta of massive vector fields

  1. Jan 8, 2008 #1
    Are the W+,W- and Z0 the field quanta of the massive charged vector fields?????????
    ie Proca fields
     
  2. jcsd
  3. Jan 8, 2008 #2

    olgranpappy

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    They are massive and they are gauge fields (electroweak force). but the Z0 is not charged.
     
  4. Jan 8, 2008 #3

    blechman

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    "Proca" fields are massive, spin-1 bosons. These objects are not unique. W and Z bosons are examples of these things. So is the rho meson in hadron physics. They are each their own separate Proca field.
     
  5. Jan 8, 2008 #4
    but hadrons are not fundamental
    but thanks for clearing the doubt regarding w bosons
     
  6. Jan 8, 2008 #5

    blechman

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    what does "fundamental" have to do with anything???
     
  7. Jan 8, 2008 #6

    yes but Z0 field can be written as a linear combination of W+ and W- fields
    like in scalar fields right?????????????to get a real valued field
     
  8. Jan 8, 2008 #7

    blechman

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    what I mean by my above post is that "Proca" has nothing to do with "fundamental" - it's just the Lagrangian for a massive, spin-1 particle. The deuteron, for example, can be described by a proca field, as long as you're not interested in the substructure of the deuteron (ex: problems in atomic or molecular physics)!
     
  9. Jan 8, 2008 #8

    blechman

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    NO!!!! The Z boson is NOT a linear combination of the charged W bosons! It is its own thing.
     
  10. Jan 8, 2008 #9

    olgranpappy

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  11. Jan 8, 2008 #10
    wait a minute this is getting a bit confusing in nucleur physics the pions are described by complex scalar fields and over there the neutral pion is decribed by the field 1/2*(phi+phi*),i think i read this in JJ Sakurai advanced QM
    Plz confirm
     
  12. Jan 8, 2008 #11

    blechman

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    You are mis-informed! The neutral pion is not related to the charged pions - it is a linearly independent scalar field.

    I think you're getting confused with the following: the 3 pions form an isospin-1 field (3 components), call them [itex]\pi_1,\pi_2,\pi_3[/itex]. now you can write:

    [tex]\pi^{\pm}=\frac{1}{\sqrt{2}}(\pi_1\pm i\pi_2)[/tex]

    while [itex]\pi^0 = \pi_3[/itex]. Here the sign corresponds to the charge.

    Now for the W bosons, you can also write [itex]W^\pm\propto(W_1\pm iW_2)[/itex] while the Z-boson is related to [itex]W_3[/itex], although the Z boson also has hypercharge so it's more complicated than the [itex]\pi^0[/itex].

    Does that help?
     
  13. Jan 8, 2008 #12

    blechman

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    Also, in the quark model, remember that the charged pions are (u-dbar) and (d-ubar), while the neutral pion is (u-ubar)+(d-dbar) - so these are not the same thing!
     
  14. Jan 8, 2008 #13
    thanks a lot belchman
    i know i was a confused
     
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