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Tensorial Methods and Renormalization in Group Field Theories

Sylvain Carrozza (Autor)

Buch | Hardcover

XV, 226 Seiten

2014 | 2014
Springer International Publishing (Verlag)
978-3-319-05866-5 (ISBN)

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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.

Sylvain Carrozza studied physics and mathematics at the École Normale Supérieure de Lyon. He then completed his doctoral studies in theoretical physics, with joint affiliation at the University of Paris-Sud and at the Max Planck Institute for Gravitational Physics. He is currently a postdoctoral researcher at the University of Aix-Marseille.

Motivations and Scope of the Present Work.- Two Paths to Group Field Theories.- Colors and Tensor Invariance.- Large N Expansion in Topological Group Field Theories.- Renormalization of Tensorial Group Field Theories: Generalities.- Super-Renormalizable U(1) Models in Four Dimensions.- Just-Renormalizable SU(2) Model in Three Dimensions.

Erscheint lt. Verlag	25.4.2014
Reihe/Serie	Springer Theses
Zusatzinfo	XV, 226 p. 51 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	510 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Colored GFT • Group Field Theory • Large Cutoff Behavior • lattice gauge Theory • Loop Quantum Gravity • Quantum Gravity • Renormalization Group Transformations • Spin Foam • Tensorial GFT
ISBN-10	3-319-05866-5 / 3319058665
ISBN-13	978-3-319-05866-5 / 9783319058665
Zustand	Neuware