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Scalar fields and the Higgs boson

  1. Sep 6, 2015 #1
    This is more of a QFT question, so the moderator may want to move it to another forum.

    The simplest example of a QFT that I learned was the scalar field; in Sakurai's 1967 text book.
    I know the Higgs is a J=0 particle. Is it described by the simple scalar field discussed in Sakurai's text? I ask because I hear about the complexity of the Higgs and that there may be up to 5 Higgs bosons.

    Your thoughts and comments are welcome.
  2. jcsd
  3. Sep 7, 2015 #2


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    Science Advisor

    Yes, if we write the fields of the Standard Model that correspond to particles of definite mass. Then there is a real scalar field that corresponds to the physical Higgs boson.

    However, if instead we use fields that have definite transformation properties under the gauge symmetries, then the Higgs field is a complex doublet of the SU(2) gauge symmetry (and also transforms under the U(1) hypercharge symmetry); that is, two complex scalar fields, equivalent to four real scalar fields. After spontaneous symmetry breaking, three of these fields end up as the longitudinal components of the massive ##W^\pm## and ##Z^0## gauge fields, and the fourth is the field corresponding to the Higgs particle.

    In some extensions of the Standard Model, there are two Higgs doublets, equivalent to 8 real scalar fields. 3 of these end up as the longitudinal ##W^\pm## and ##Z^0##, and the remaining 5 are scalar bosons. Three have electric charge zero, and the other two have electric charge ##\pm1## (in units of the electron charge).
    Last edited: Sep 7, 2015
  4. Sep 7, 2015 #3
    Thank you Avodyne. You answered my question and anticipated my next question. It's going to take me a while to digest this information. It is very helpful. Thank you.
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