Generalized Coherent States and the U(n) Lie Group

Abstract

In this paper we study the generalized coherent states (g.c.s.) in n-dimensional space. Their annihilation operators consist of linear combinations of the annihilation operators a_l, and their coherent states are the product of the simple coherent states. All the known annihilation operators which have been studied as yet, and also the magnetic ones, are special cases of these operators. The new operators A_k⁺A_m form the Lie algebra U(n) of the Lie group U(n). Finally, instead of the operators a_l and a_l⁺ we can use the new operators, which depend on a complex parameter.