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Let's assume that we have integer spin interaction theory (EM field, linearized gravity, arbitrary gauge spin s theory). How to prove the consequence that in interaction theory with spin $s = 2n$ two identical particles (equal spins, masses, all charges etc) are attracted (like gravity), while in $s = 2n + 1$ theory they are repelled (like in EM interactions)?

Andrew McAddams
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  • Maybe you will be intereted by this short answer, although some interesting precisions should be added.. – Trimok Jun 14 '14 at 12:02
  • @Trimok : thank you for the answer and for the reference. But can be earned the general result from my question? – Andrew McAddams Jun 15 '14 at 09:35
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    The general idea, is that, for a field with a spin $s$ interaction, you have, in the Lagrangian, a time derivative term of spatial components which is (roughly) $\partial_0 A^{{i_1 i_2 ...i_s}} \partial^0 A_{{i_1 i_2 ...i_s}}$. We want to have a positive quantity, which is $(\partial_0 A^{{i_1 i_2 ...i_s}})^2$. To go from the first expression to the last expression, you have a factor $g^{00} g^{i_1 i_1} g^{i_2 i_2}...g^{i_s i_s}$, which is equal to $(-1)^s$. – Trimok Jun 17 '14 at 08:18

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