I'm interested in the following action for a relativistic point particle of mass m:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]S = \int d\tau (e^{-1}\dot{x}^2 - em^2)[/itex]

where [itex]e = e(\tau)[/itex] is an einbein along the particle's world-line. If we reparametrize the world-line according to

[itex]\tau \to \overline{\tau}(\tau) = \tau + \xi(\tau)[/itex]

then the einbein apparently changes according to

[itex]e(\tau) \to e(\tau) + \frac{d}{d\tau}(e(\tau)\xi(\tau))[/itex]

However, I can't seem to understand where the term [itex]e(\tau)(d/d\tau)\xi(\tau)[/itex] comes from in this. A Taylor expansion of [itex]e(\tau + \xi(\tau))[/itex] would seem to give me only [itex]e(\tau) + \xi(\tau)(d/d\tau)e(\tau)[/itex] plus higher-order terms.

Can anyone explain to me where the extra term [itex]e(\tau)(d/d\tau)\xi(\tau)[/itex] comes from? Is there something particularly special about the einbein that gives rise to this term?

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

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!

# Action for the relativistic point particle

Loading...

Similar Threads - Action relativistic point | Date |
---|---|

The Action[s] of relativistic particle | Oct 11, 2014 |

Relativistic Action: Mathematics | May 22, 2014 |

Derivation of relativistic motion equations from action | Apr 22, 2012 |

Relativistic non-instantaneous action-at-a-distance interactions | Jan 28, 2007 |

Relativistic Action | Nov 16, 2006 |

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