Lagrangian of superfluid He3

Abstract

This paper presents a phenomenological Lagrangian that fully describes the dynamics of any homogeneous phase of superfluid He3, unitary or not, omitting relaxation. This Lagrangian is built by using the concept of a local SO(3)×SO(3)×U(1) symmetry. The spin and angular momentum play the role of gauge fields. We derive the Leggett equations for spin and orbital dynamics from the equations of motion, for both the A and the B phase. This Lagrangian not only enables us to describe both the spin and orbital dynamics of superfluid He3 in a unified fashion, but can also be used for finding the dynamics in any experimental situation. Furthermore, it can describe the dynamics of the magnitude, as well as of the orientation of the order parameter, and thus it can be used to describe the dynamics of the A-B phase transition. © 1988 The American Physical Society.