# Tag Info

## New answers tagged field-theory

1

For instance, a Lagrangian $L = \partial_i \phi \partial^i \phi + m^2\phi^2$ has the same equation of movement that the Lagrangian $L' = \partial_i \phi \partial^i \phi + m^2(F\phi - \frac{F^2}{2})$. The Euler-Lagrange equation for $L'$ simply give $\Box \phi +m^2F=0$ and $F = \phi$, so we have $\Box \phi +m^2\phi=0$, which are the Euler-Lagrange ...

2

When you have a matrix $\Phi = \begin{pmatrix} \phi_1\\ \phi_2\end{pmatrix}$, with one column and two rows, and its transpose matrix $\Phi^T = \begin{pmatrix} \phi_1 & \phi_2\end{pmatrix}$, with one row and two columns, the product of the two matrix $\Phi^T \Phi$ is a matrix $P$ with one column and one row: \$P =\Phi^T \Phi = \begin{pmatrix} \phi_1 ...

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