Open AccessSpectral Analysis of Volume Operators in Loop Quantum Gravity for Kinematical Case
Author(s) -
Ignatius Sebastian,
I. Husin,
Seramika Ariwahjoedi,
Freddy P. Zen
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1245/1/012086
Subject(s) - loop quantum gravity , operator (biology) , spin foam , quantum gravity , ladder operator , physics , mathematical physics , immirzi parameter , eigenvalues and eigenvectors , mathematics , spin network , momentum operator , quantum , regularization (linguistics) , quantum mechanics , compact operator , computer science , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , extension (predicate logic) , gene , programming language
Loop Quantum Gravity has become one of the alternative solutions to quantum gravity. This formulation introduced geometrical operators which successfully used to model that in the quantum scale, the space is actually discretized in the order of Planck length. These operators are area and volume operator. The regularization process of these operators came from the classical definition of area and volume, thus, the eigenvalues of area operator and volume operator are respectively the area and volume of the space. However, there exists two types of volume operator, the Ashtekar-Lewandowski operator and the Rovelli-Smolin operator. The significant difference between these two operators is the fact that Ashtekar-Lewandowski operator is sensitive to the direction of the spin networks link, while Rovelli-Smolin operator is not. This difference will produce different spectral. In this article, we compare the resulting spectral of the two volume operators, where both of them is used to calculate the volume of the monochromatic 4-valent and 6-valent spin network for the kinematical case.