There is a step that bothers me in my book (Ryder) on QFT and I can't seem to figure it out. It concerns the (spatial) rotation of the spatial part of the Dirac four current:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\bar{\psi} \gamma \psi [/tex]

The crucial step here is

[tex]\frac{1}{4}(\vec{\sigma} \cdot \vec{\theta}) \vec{\sigma}(\vec{\sigma} \cdot \vec{\theta}) = -\vec{\theta} \times \vec{ \sigma} [/tex]

With [itex]\vec{\theta}[/tex] the (infinitesimal) rotation and [itex]\vec{\sigma}[/tex] the vector consiting of the three Pauli matrices.

I tried writing it in tensor notation and using the commutation reltaions as in the supplied tip, but I can't figure it out... Can anybody show me this?

**Physics Forums - The Fusion of Science and Community**

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

# Rotating Dirac particle current

Loading...

Similar Threads - Rotating Dirac particle | Date |
---|---|

I Macroscopic rotation from spin flipping? | Mar 3, 2018 |

I Rotational transitions | Jan 19, 2018 |

I Why this system has a rotational symmetry in Dirac equation? | Dec 23, 2017 |

I How is Graphene's Hamiltonian rotationally invariant? | Mar 2, 2017 |

Dirac Lagrangian not invariant under rotations? | Jun 24, 2006 |

**Physics Forums - The Fusion of Science and Community**