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basic_tools:symbols [2018/03/28 14:09]
jakobadmin
basic_tools:symbols [2018/04/15 10:20] (current)
ida
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\} \\
basic_tools/symbols.txt ยท Last modified: 2018/04/15 10:20 by ida