A More Complicated Field Theory

 

$$\begin{eqnarray*}\mathcal{L} &=& \frac{1}{8} {F^{\mathcal{A}}}_{\mu\nu} {F_{\ma... ...ambda^2\left(\boldsymbol{\phi}\cdot\boldsymbol{\phi} \right)^2 \end{eqnarray*}$$

• Observe that energy assumes a minimum for F = G = L = R = and
  
  $$\boldsymbol{\phi} = \left( \begin{array}{c} 0 \\ r \end{array} \right)$$
  
  
  where $r\in \mathbb{R}$. This is called spontaneous symmetry breaking,   a phenomenon known from the theory of magnetism, for example.
• Expanding $\boldsymbol{\phi}$ around that point and plugging it into $\mathcal{L}$ generates the following fields:
  
  $$\begin{eqnarray*}W_{\mu\mp} &=& \frac{A^1{}_\mu \pm A^2{}_\mu}{\sqrt{2}} \quad... ...x{of mass $Gr$ } \\ \nu &=& L^A{}_0 \quad\hbox{of mass $0$ } \end{eqnarray*}$$
  
  

Field $\boldsymbol{\phi}$ itself becomes associated with a field $\sigma$ of mass $2\lambda r$. This is called the Higgs   field and still awaits an experimental discovery. All other fields, W, Z, A, e and $\boldsymbol{\nu}$ have been already discovered.

Recent Kamiokande   measurements indicate that $\boldsymbol{\nu}$ has   mass.

All these results are classical, i.e., the Salam-Weinberg-Glashow equations are treated like classical fields in all those symmetry breaking calculations. Quantum interpretations (i.e., particles) are then squeezed from classical results upon a certain amount of handwaving.