# A Identification of particle and antiparticle in lagrangian

1. Dec 5, 2016

### spaghetti3451

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. Dec 5, 2016

### Orodruin

Staff Emeritus
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.