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11.P: Exercises

  • Page ID
    1261
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    1. Noting that \( \alpha_i\) and \( n\) eigenvalues \( +1\) , and \( -1\) , where \( \partial_\mu\,j^{\,\mu} = 0,\) where \( j^{\,\mu}\) is a 4-vector field, then $ \int d^3 x\,j^{\,0}
$ is Lorentz invariant, where the integral is over all space, and it is assumed that \( j^{\,\mu}\rightarrow 0\) as $ \vert{\bf x}\vert\rightarrow
\infty$ .
    2. Verify that \ref{1168} is a solution of \ref{1167}.
    3. Verify that the \( \Sigma_i\) , defined in \ref{1189}, satisfy the standard anti-commutation relations for Pauli matrices: i.e., $ \{\Sigma_i, \Sigma_j\} = 2\,\delta_{ij}.
$

    Contributors

    • Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)

      \( \newcommand {\ltapp} {\stackrel {_{\normalsize<}}{_{\normalsize \sim}}}\) \(\newcommand {\gtapp} {\stackrel {_{\normalsize>}}{_{\normalsize \sim}}}\) \(\newcommand {\btau}{\mbox{\boldmath$\tau$}}\) \(\newcommand {\bmu}{\mbox{\boldmath$\mu$}}\) \(\newcommand {\bsigma}{\mbox{\boldmath$\sigma$}}\) \(\newcommand {\bOmega}{\mbox{\boldmath$\Omega$}}\) \(\newcommand {\bomega}{\mbox{\boldmath$\omega$}}\) \(\newcommand {\bepsilon}{\mbox{\boldmath$\epsilon$}}\)

    This page titled 11.P: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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