Magnetically Driven Superconducting Pairing Interaction in the Two-Dimensional Hubbard Model within a Spin-Rotationally Invariant Approach

The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.