Assuming that a massive spin-1 particle has momentum only in the z-direction, the polarization vectors are given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\varepsilon_{\mu}(J_z = +1) = (0,-\frac{1}{\sqrt{2}},-\frac{i}{\sqrt{2}},0 )[/tex]

[tex]\varepsilon_{\mu}(J_z = 0) = (\frac{p}{m},0,0, \frac{E}{m})[/tex]

[tex]\varepsilon_{\mu}(J_z = -1) = (0,\frac{1}{\sqrt{2}},-\frac{i}{\sqrt{2}},0 )[/tex]

The so-called spin-sum is the claimed to be

[tex]

\sum\limits_{J_z = -1,0,+1} \varepsilon_{\mu}\varepsilon_{\nu}^* = g_{\mu\nu} + \frac{p_{\mu}p_{\nu}}{m^2}

[/tex]

I absolutely dont understand how this spin-sum is evaluated.

What does [itex]\varepsilon_{\mu}\varepsilon_{\nu}^*[/itex] even exactly mean? Is it a scalar product between two of the three above polarization vectors, or is it a "tensor-product" between the components of a single polarization vector which results in a 4x4 matrix and one has finally to sum all such matrices for the three possible values of [itex]J_z[/itex]?

I would really appreciate it if somebody can explain to me what this spin-sum exactly means and how it is evaluated step-by-step.

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

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!

# Demystification of the spin-sum for massive spin-1 particles

Tags:

Loading...

Similar Threads for Demystification spin massive |
---|

A I need a spherically symmetric spin-dependent NN potential |

I Spin vs Helicity conservation |

A Nuclear spin of Fluorine 19 |

B Is neutrino spin-parity 1/2+ or 1/2-? |

A How do we know the spins of elementary particles? |

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