The Solution of Electromagnetic Field in AdS² with Factrization Method

Abstract

In this paper, we first study the Laplace equation in AdS 2 space with electromagnetic field. In order to construct the corresponding Schrödinger equation, we write the metric and vector potential in suitable way. So, in that case, we face with Schrödinger equation in AdS 2 space. By using factorization method, we factorized the second order equation in terms of first order equations. These first order operators show that our system has a some shape invariance condition. It leads us to obtain the supercharges and corresponding commutative relation. Finally, we show that these supercharges will be form of generators of algebra.