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Spectral Analysis of Volume Operators in Loop Quantum Gravity for Kinematical Case
Sebastian I.a, Husin I.a, Ariwahjoedi S.a, Zen F.P.a
a Theoretical Physics Laboratory, THEPI Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© Published under licence by IOP Publishing Ltd.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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Alternative solutions,Geometrical operators,Loop quantum gravity,Planck length,Quantum gravity,Quantum scale,Regularization process,Spin networks[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1088/1742-6596/1245/1/012086[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]