New Approaches to Nuclear Pairing Problem through the Pfaffian and Grassmann Algebra(Research)

Abstract

The Hartree-Fock-Bogoliubov (HFB) theory, an extended theory of the Bardeen-Cooper-Schrieffer theory, is rich in physical and mathematical structures. Nuclear physicists have struggled to find compact formulae to evaluate HFB transition matrix elements of many-body operators, which handle the pairing correlations. A recent breakthrough has brought us a new formula in terms of the Pfaffian. In the derivation, the Grassmann algebra and the Fermion coherent states were employed. These findings have opened up a new way to tackle the quantum many-body problems in the presence of the pairing.