Coherent-State Approach for Majorana representation

By representing a quantum state and its evolution with the majorana stars on the Bloch sphere, the Majorana representation (MR) provide us an intuitive way to study a physical system with SU(2) symmetry. In this work, based on coherent states, we propose a method to establish generalization of MR for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general MR for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg-Weyl, SU(2) and SU(1,1), and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.