Since the interaction is invariant under the interchange of two particles it means for example that we have $$ \langle \mu\nu|\hat{v}|\mu\nu\rangle = \langle \nu\mu|\hat{v}|\nu\mu\rangle, $$ or in the more general case $$ \langle \mu\nu|\hat{v}|\sigma\tau\rangle = \langle \nu\mu|\hat{v}|\tau\sigma\rangle. $$