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4

Yes, your expectations seem reasonable when thinking of the Higgs mechanism induced mass, as explained by @nmoy. However, note that one needs to be careful in defining what one means by "mass" at high temperatures. A theory at finite (non-zero) temperature breaks Lorentz invariance. There are multiple ways to think of this: There is a preferred frame, ...

4

In the Standard Model, fermions are given their mass through yukawa terms, described by the Lagrangian: $$\mathcal{L}_{\mathrm{F}} = \overline{\psi} \gamma^{\mu} D_{\mu} \psi + y_{\psi} \overline{\psi} \phi \psi$$ Where $y_\psi$ is the yukawa coupling and $\phi$ is the Higgs field. At this stage, much like the gauge bosons, the fermions do not yet have ...

0

The error is that $\gamma_5$ doesn't intrinsically change sign under parity. Also, don't forget that under parity the spatial components of $W_\mu$ change sign. And also $\gamma^0 \gamma^\mu \gamma^0 \neq \gamma^\mu$.

2

For anyone with similar problems: The following observation has helped me immensly: We have in fact four particles directly related to an electron: A left-chiral electron $\chi_L$, with isospin $-\frac{1}{2}$ and electric charge $-e$, A right-chiral anti-left-chiral-electron $(\chi_L)^c=\chi_R$ with isospin $\frac{1}{2}$, electric charge $+e$ A ...

3

Roughly sketched, for the quantized Dirac field one has: $$\hat\psi(x)\sim \int d\mathbf{p}\, \sum_r \bigg[ u^{r}(p)\, \hat a^r_\mathbf{p}\,e^{-ipx}+v^{r}(p)\, {\hat b^r_\mathbf{p}}^\dagger e^{ipx}\bigg],$$ where $r=\pm1$ denotes helicity. The ${\hat a^r_\mathbf{p}}^\dagger$ operator creates a helicity-$r$ particle state when it ...

2

We then talk about a left-chiral electron we do it in an informal way, you are correct that a massive particle cannot be inherently chiral. To see this, let us remember that he handedness of an elementary particle depends on the correlation between its spin and its momentum (helicity). If the spin and momentum are parallel, the particle can be said to be ...

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