Factorization of Operators Evolved with the Similarity Renormalization Group

The Similarity Renormalization Group (SRG) flow equations are a series of unitary transformations which can be used to to achieve different patterns of decoupling in a Hamiltonian. An SRG transformation applied to internucleon interactions leads to greatly improved convergence properties.\footnote{S.K. Bogner, R.J. Furnstahl, and R.J. Perry, Phys. Rev. C 75 (2007) 061001.} A principal advantage of SRG transformations is that all operators can be consistently transformed, so that all observables are invariant. Calculations of the two-body momentum-distribution reveal an apparent factorization of the unitary transformation, \(U(k,q) \approx K(k)Q(q)\) for \(k\ll\lambda\) and \(q\gg\lambda\). The emergence of a nonrelativistic operator product expansion and factorization will be discussed.