In quantum mechanics, the Schrieffer-Wolff transformation (SW, also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. In the talk a geometric interpretation of the SW is presented [1] as a local coordinate chart in the space of hermitian matrices near the degeneracy stratum. Inspired by this approach, the splitting of the eigenvalues of a perturbation is interpreted in terms of the distancing from the degeneracy stratum. The physical examples range widely, including problems from condensed matter physics and quantum error correction.

 

[1] Joint work with György Frank, Dániel Varjas, András Pályi