Tensorial Methods and Renormalization in Group Field Theories
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Beschreibung
The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and, on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs, and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.
The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.
Nominated as an outstanding Ph.D. thesis by Université Paris-Sud at Orsay, France Provides pedagogical reviews of both colored and tensorial group field theories Gives a detailed introduction in the first three chapters to the concepts and assumptions entering the technical discussions of the later chapters Gathers recent results on the asymptotics and renormalization of group field theories in full technical detail, material not available in any other book or review (the original articles being scattered over several journals) Includes supplementary material: sn.pub/extras
Autor*in
Sylvain Carrozza
Themen in »Tensorial Methods and Renormalization in Group Field Theories«
Colored GFT Group Field Theory Large Cutoff Behavior Lattice Gauge Theory Loop Quantum Gravity Quantum Gravity Renormalization Group Transformations Spin Foam Tensorial GFT