In his early career at Princeton University Coleman worked on the problem of valence fluctuations in solids. In the 1960s the physicist John Hubbard introduced a mathematical operator, the "Hubbard operator" for describing the restricted fluctuations in valence between two charge states of an ion. In 1983 Coleman invented the slave boson formulation of the Hubbard operators, which involves the factorization of a Hubbard operator into a canonical fermion and a boson X_{\sigma 0}= f^{\dagger}_{\sigma}b. The use of canonical fermions enabled
