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What do we mean with spontaneous symmetry breaking $SU(2) \times U(1) \to U(1)$ in particle physics?

I think my problem is with group theory. I understand that within the Standard Model the Lagrangian is invariant under $SU(2)_{L}\times U(1)_{Y}$ symmetry, but I do not understand what we mean (...
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43 views

Motivation for Weinberg angle in electroweak gauge interaction?

Suppose I have the following lagrangian If we only focus on the neutral current in the lagrangian: Where $L$ is defined as: And $Y_L$,$Y_{R}^{\nu}$,$Y_{R}^{e}$, are the hypercharge values of the ...
1
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40 views

Global $U(1)$ Symmetry in GSW Model

Consider the theory of a single generation of $e, \nu_L$ matter content. The initial lagrangian is $$ \mathcal{L} = i\bar{\ell}\not \partial\ell + i\bar{e}_R\not \partial e_R \tag{1} $$ where $$ ...
2
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2answers
255 views

$SU(2)$ Invariant Lagrangian

Consider two arbitrary scalar multiplets $\Phi$ and $\Psi$ invariant under $SU(2)\times U(1)$. When writing the potential for this model, in addition to usual terms like $\Phi^\dagger \Phi + (\Phi^\...
2
votes
1answer
105 views

Hydrogen and the neutron

I have a question about Hydrogen and the neutron. So a neutral hydrogen atom has structure ${}^1H\equiv[p^+ e^-]$, a bound proton and electron. From a quantum theoretical viewpoint, one would write ...
1
vote
1answer
559 views

Is the weak interaction Lagrangian invariant under parity transformations?

The weak interaction term in the Lagrangian reads $$ \bar \Psi \gamma_\mu P_L \Psi W^\mu. $$ Under parity transformations, because of $\Psi \rightarrow \gamma_0 \Psi$ and $\gamma_5 \rightarrow -...