The Matrix Elements of Area Operator in (2+1) Euclidean Loop Quantum Gravity

Abstract

Abstract In this article we discuss the matrix elements of area operator in (2+1) Euclidean Loop Quantum Gravity. The Euclidean signature is chosen because it has the same group as (3+1) Lorentzian Loop Quantum Gravity that is SU (2). The techniques used follows what has been done on the volume operator in (3+1) Lorentzian Loop Quantum Gravity. Although both are referred to as volume operator, they both have significantly different forms, so the initial steps of the discussion will be different. The result show that we can express the matrix elements in terms of standard recoupling scheme basis.