MATRIX ELEMENTS OF AREA OPERATOR IN (2+1) EUCLIDEAN LOOP QUANTUM GRAVITY

• Main Author: Fahmi, Khazali
• Format: Theses
• Language: Indonesia
• Subjects: Fisika
• Online Access: https://digilib.itb.ac.id/gdl/view/45710
• Institution: Institut Teknologi Bandung

One of the problems in theoretical physics is the attempt to make the theory of general relativity leads to the quantum properties, which is called quantum gravity theory. An approach used in quantizing the gravitational field is to use canonical formulations. The general relativity theory (GRT) initially used metrics as dynamic variables. However, GRT can also be expressed in other variables, which is named the Ashtekar variable that leads to an existing particle theory. The steps are used in particle theory can be used to quantify the gravitational field even if it is not completely. Gravity as a manifestation of spacetime itself carries the same problems as quantizing geometry. Of course geometrical quantities such as volume, area and length are the main quantities in the quantization problem of the gravitational field. Various calculations have been carried out in the object and obtained that the geometry operator has a discrete spectrum. Geometry operator can be represented in the matrix and carried out matrix elemen from the operator which is assigned this thesis. Here, an analysis of the matrix elements of a area operator in dimension (2+1) with Euclidean signatures has been carried out and the results can be stated in 6j-Symbols. The Euclidean signature is chosen because it has the same gauge group as the TRU in dimension (3+1) with the Lorentzian signature which is the SU(2) group..