[nr3 gP gn4 Nri tTiT21

+ 2iei3j-{gp + gn)<f>j + 2iei3j(gp - gn)T3<Pj

We get three equations, one for each v.

i = 1 - i(gp - gn)T2<t>3 + iV2g+T3<p2 + i(gP + 9n)<t>2 - i{gP - 9n)T302 + i\/2g+T2(j>3 = 0

i = 2 i(gp -gn)Ti<t>3 ~ iV2g+T3<j>i +i{gP + gn)4>\ (9.109)

i = 3 iV2g+ [t20i - Tifo] + iV2g+ [ti</>2 - t24>i] = 0 . The third equation is satisfied identically; the first two are satisfied for any fa if gP-9n = V2g+ gP + gn=0 . (9.110)

Hence

and the interaction can be written

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