The equation for a massive spin 1 particle is given by the Proca equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \partial_\mu(\partial^\mu A^\nu - \partial^\nu A^\mu)+ \left(\frac{mc}{\hbar}\right)^2 A^\nu=0 [/tex]

My question is why this equation? In particular, why can't it be like this instead:

[tex] \partial_\mu(\partial^\mu A^\nu +2 \partial^\nu A^\mu)+ \left(\frac{mc}{\hbar}\right)^2 A^\nu=0 [/tex]

The Lagrangian is given by:

[tex] \mathcal{L}=-\frac{1}{16\pi}(\partial^\mu A^\nu-\partial^\nu A^\mu)(\partial_\mu A_\nu-\partial_\nu A_\mu)+\frac{m^2 c^2}{8\pi \hbar^2}A^\nu A_\nu [/tex]

and again, why can't the derivative terms instead be:

[tex]X\partial_\nu A_\mu \partial^\nu A^\mu+Y\partial_\nu A^\nu \partial^\mu A_\mu +Z\partial_\nu A^\mu \partial_\mu A^\nu[/tex]

for arbitrary real numbers X,Y, and Z?

The answer can't be that there is a U(1) symmetry, because the mass terms don't obey the U(1) symmetry.

**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!

# Form of the spin 1 equation

Loading...

Similar Threads - Form spin equation | Date |
---|---|

B Change in the form of energy | Feb 12, 2018 |

A What form of the Schrodinger equation do you use for intensity? | Feb 9, 2018 |

I Representing a Hamiltonian in an operator form | Feb 5, 2018 |

Two hydrogen atom with same spin can form H_2? | Nov 29, 2011 |

Explicit form for representing two spin 1/2 system | Apr 3, 2011 |

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