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basic_tools:symbols

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 basic_tools:symbols [2018/03/28 16:09]jakobadmin basic_tools:symbols [2018/04/15 12:20] (current)ida Both sides previous revision Previous revision 2018/04/15 12:20 ida 2018/03/28 16:09 jakobadmin 2018/03/28 16:09 jakobadmin 2018/03/28 16:09 jakobadmin 2018/03/28 16:00 jakobadmin 2018/03/28 16:00 jakobadmin 2018/03/21 10:39 jakobadmin 2018/03/21 10:39 jakobadmin 2018/03/21 10:38 jakobadmin 2018/03/21 10:38 jakobadmin 2018/03/21 10:37 jakobadmin 2018/03/21 10:37 jakobadmin created 2018/04/15 12:20 ida 2018/03/28 16:09 jakobadmin 2018/03/28 16:09 jakobadmin 2018/03/28 16:09 jakobadmin 2018/03/28 16:00 jakobadmin 2018/03/28 16:00 jakobadmin 2018/03/21 10:39 jakobadmin 2018/03/21 10:39 jakobadmin 2018/03/21 10:38 jakobadmin 2018/03/21 10:38 jakobadmin 2018/03/21 10:37 jakobadmin 2018/03/21 10:37 jakobadmin created Line 1: Line 1: ====== Symbols ====== ====== Symbols ====== + + * Derivatives with respect to the four-vector $x^{\mu}=(ct,​\vec{x})$ are denoted by + \begin{eqnarray} + \partial_{\mu}\equiv {\partial\over \partial x^{\mu}} + =\left({1\over c}{\partial\over\partial t},​\vec{\nabla}\right). + \end{eqnarray} + * Space-time indices are labelled by Greek letters ($\mu,​\nu,​\ldots=0,​1,​2,​3$) ​ + * Latin indices are used for spatial directions ($i,​j,​\ldots=1,​2,​3$). ​ + * Moreover, $\sigma^{\mu}=(\mathbf{1},​\sigma^{i})$ where $\sigma^{i}$ are the Pauli matrices $$+ \sigma^{1}=\left( + \begin{array}{rr} + 0 & 1 \\ + 1 & 0 + \end{array} + \right), \quad \sigma^{2}=\left( + \begin{array}{rr} + 0 & -i \\ + i & 0 + \end{array} + \right), ​ \quad + \sigma^{3}=\left( + \begin{array}{rr} + 1 & 0 \\ + 0 & -1 + \end{array} + \right).$$ + + + + + **Math Symbols** \begin{align} \begin{align} &​\mathbb{N} = \{0, 1, 2, 3, \ldots\} \\ &​\mathbb{N} = \{0, 1, 2, 3, \ldots\} \\