Right-handed fermions

We consider the general triangle diagram shown in Fig. 9.5, bearing in mind that we must include both the left-handed and right-handed fermion contributions, and also that each fermion labelled i,j,k can either flow towards or away from a particular vertex. (In Fig. 9.5 we show only the left-handed fermions. Similar diagrams occur for the right-handed ones.)... 

In similar fashion the right-handed fermions give... 

P is a permutation of atoms with the same spin and necessarily must be even because of the restriction [V"(R) is the potential energy] [23]. The exact density matrix will then appear both on the left-hand side of Eq. (5) and implicitly in the restriction on the right-hand side of Eq. (6). This implies that there exists a restriction which does not have a fermion sign difficulty. In the fixed-node approximation, a trial density matrix is used for the restriction on the right-hand side of Eq. (6). 

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