The radial equation of the Rarita Schwinger field in spherically symmetric spacetimes
Chun-Hung, Chen1*, Hing-Tong Cho1
1Department of Physics, Tamkang University, New Taipei City, Taiwan
* presenting author:Chun-Hung Chen, email:899210057@s99.tku.edu.tw
Starting with the eigenvalue problem for spin 3/2 fields on N-spheres, we find that there are two set of eigen-spinor-vectors modes, which call Rarita-Schwinger modes and Non-Rarita-Schwinger modes. By using the linear combination of these mode functions direct product with the eigen-spinors and using the Weyl gauge, we can obtain the radial equation for the Rarita-Schwinger field in a spherically symmetric spacetime.

We find that different modes on N-spheres leads to different radial equations in D=N+2 dimensional spherically symmetric spacetimes. The radial equation related to the Non-RS mode on N-sphere give us the spin 3/2 field equation which are consistent with [1][2] in the 4-dimensional case. And the one related to the RS modes is similar to the radial equation for spin 1/2 fields on spherically symmetric spacetimes. [3]

[1] P. C. Aichelburg and R. Gϋven, Phys. Rev. D 24,2066 (1981)
[2]G. F. Torres del Castillo and G. Silva-Ortigoza, Phys. Rev. D 46, 5395 (1992)
[3]H. T. Cho, A.S. Cornell, Jason Doukas, and Wade Naylor Phys. Rev. D 75, 104005 (2007)


Keywords: Rarita-Schwinger field , radial equation, spherically symmetric spacetimes