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A Identification of particle and antiparticle in lagrangian

  1. Dec 5, 2016 #1
    Lagrangians that include a particle field and its corresponding antiparticle field always have the particle field and the antiparticle field in the same terms.

    For example, in the theory of a complex scalar boson ##\phi##, the Lagrangian is a function of ##\phi^{*}\phi##, and not of ##\phi## and ##\phi^{*}## separately.

    Also, in the theory of a Dirac fermion ##\psi##, the Lagrangian is a function of ##\bar{\psi}\psi##, and not of ##\psi## and ##\bar{\psi}## separately.

    This makes it difficult to see if the fermion is ##\psi## and the antifermion is ##\bar{\psi}## or if, the fermion is ##\bar{\psi}## and the antifermion is ##\psi##.

    Is there a way to solve this problem?
     
  2. jcsd
  3. Dec 5, 2016 #2

    Orodruin

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    First of all, those are not particle and antiparticle fields. The field ##\phi## contains the creation operator of an antiparticle and the destruction operator of a particle and vice versa.

    Second, it is not necessary that they always appear like that - as long as you have other fields in the term that ensure invariance under gauge transformations. Compare with the Yukawa couplings with a Higgs doublet, which couples different fields.
     
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