The Matrix Elements of Area Operator in (2+1) Euclidean Loop Quantum Gravity
Khazali Fahmi (a*), Freddy Permana Zen (a,b)
a) Theoretical Physics Laboratory, THEPI Division, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132, West Java, Indonesia.
*khazali.fahmi[at]students.itb.ac.id
b) Indonesian Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10 Bandung 40132, West Java, Indonesia.
Abstract
In this article we discuss the matrix elements of volume 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 signi cantly di erent forms, so the initial steps of the discussion will be di erent. The result show that we can express the matrix elements in terms of standard recoupling scheme basis.
Keywords: Loop Quantum Gravity, Volume operator.
Topic: Theoretical High Energy Physics