Suppose we are given this definition of the wedge product for two one-forms in the component notation:(adsbygoogle = window.adsbygoogle || []).push({});

$$(A \wedge B)_{\mu\nu}=2A_{[\mu}B_{\nu]}=A_{\mu}B_{\nu}-A_{\nu}B_{\mu}$$

Now how can we show the switch from tensor products to wedge product below:

$$\epsilon=\epsilon_{\mu_{1}...\mu_{n}}dx^{\mu_{1}}\otimes...\otimes dx^{\mu_{n}}$$

$$=\frac{1}{n!}\epsilon_{\mu_{1}...\mu_{n}}dx^{\mu_{1}}\wedge...\wedge dx^{\mu_{n}}$$

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A How to switch from tensor products to wedge product

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for switch tensor products |
---|

I Basic Q about Vector/tensor definition and velocity |

I Lie derivative of a metric determinant |

I Deduce Geodesics equation from Euler equations |

A On the dependence of the curvature tensor on the metric |

A Covariant derivative only for tensor |

**Physics Forums | Science Articles, Homework Help, Discussion**