Developpement Mathematique Et Applications De La Gravitation Quantique a Boucles

الموضوعات

علوم بحتة وطبيعية

الملخص

Loop Quantum gravity is a tentative theory to describe the quantum structure of spacetime at the Planck scale, the scale at which both general relativity and quantum theory manifest equally. The theory comes in threeversions: The canonical approach, covariant approach and geometric approach. All the approaches use the same Hilbert space, but we do not knowwhether they actually correspond to the same theory.In this thesis, I will present our main results in the loop quantum gravityprogram, all of which lie in between the three approaches. We start with describing The canonical and covariant approaches in which the notations andgeneral concepts of the theory are fixed. Then, we discuss our contributionon the length spectrum of space, the length of the tetrahedral edges. Afterthat, we investigate the quantum polyhedra and its relation to loop quantumgravity. More specifically, we discuss the quantum tetrahedron: the 4-nodeHilbert space. We finish the chapter by investigating our contribution inthe filed the quantum polyhedra: the discreteness of the area of space viaBohr-Sommerfeld quantization. Next, we investigate our deriving to the volume of space spectrum for arbitrary number of faces of the polyhedron. Weuse the idea of virtual lines together with the fact that the node Hilbertspace with valency N can be split into series of connected 4-valent nodesHilbert spaces. Then, we study the quantum pentahedron in which a nicerepresentation on phase spaces for the pentahedral atoms of space is given.Next, we investigate our works on: (a) Regge and Twisted Geometries inthe context of the loop Gravity Hilbert space and (b) Regge and TwistedGeometries in Schwarzschild Spacetime. We discuss the interesting results inwhich twisted-truncation is included in interpreting the loop gravity graph.Furthermore, the Schwarzschild Spacetime graph is well-studied. Finally, anew quantity called space density is introduced and an interpretation forgravity force is discussed.

روابط وملفات

التعريف والنوع

رقم الوثيقة

ebc6d5c0-79f7-4855-a78d-b6869c613737

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

790918_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":" Ahmida Bendjoudi","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"Noureddine Mebarki","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

French

المصدر والدورية

اسم المصدر

Developpement Mathematique Et Applications De La Gravitation Quantique a Boucles

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

Noureddine Mebarki

الإعداد

Ahmida Bendjoudi

الاقتباسات الببليوغرافية