A Fierz rearrangement rewrites a product of fermion bilinears with one spinor pairing as a sum of products with another pairing. For left-handed vector currents, it lets a charged-current four-fermion operator be compared directly with a neutral-current operator.
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The Fierz identity, named after the physicist M. Fierz, is a relation in quantum field theory that is particularly useful in the context of particle physics, especially when dealing with fermions and their bilinear forms. It provides a way to express products of bilinear forms of fermionic states in terms of a complete set of independent bilinear products.