Dirac current

**standard model of particle physics**

**matter field fermions** (spinors, Dirac fields)

1st | 2nd | 3d |
---|---|---|

up? | charm | top |

down? | strange? | bottom |

**hadron** (bound states of the above quarks)

**minimally extended supersymmetric standard model**

bosinos:

**dark matter candidates**

**Exotica**

**spin geometry**, **string geometry**, **fivebrane geometry** …

**rotation groups in low dimensions**:

see also

In the Lagrangian field theory of the Dirac field, the *Dirac current* is a conserved current whose interpretation is literally the current of the spinor particles that are the quanta of the Dirac field. Therefore the corresponding charge is *fermion number*. As such the Dirac current (or rather its chiral version) plays a key role for instance in baryogenesis.

The Dirac current is the conserved current which is associated via Noether's theorem I to the infinitesimal symmetry of the Lagrangian given by multiplying the Dirac field by a complex phase.

In the usual standard coordinates, the Dirac current is of the form

$\overline{\psi}\gamma^\mu \psi \, \iota_{\partial_\mu} dvol_\Sigma
\;\in\;
\Omega^{p,0}
\,.$

For details see at *geometry of physics – A first idea of quantum field theory* this example.

Created on November 8, 2017 at 13:58:25. See the history of this page for a list of all contributions to it.