U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Sch\"on approaches

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Sch\"on approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).