The universal coefficient theorem and quantum field theory : a topological guide for the duality seeker
著者
書誌事項
The universal coefficient theorem and quantum field theory : a topological guide for the duality seeker
（Springer theses : recognizing outstanding Ph. D. research）
Springer, c2017
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注記
"Doctoral thesis accepted by University College London, London, UK" -- T.p.
Includes bibliographical references
内容説明・目次
内容説明
This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics-one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
目次
Introduction.- Elements of General Topology.- Algebraic Topology.- Homological Algebra.- Connections: Topology and Analysis.- The Atyiah Singer Index Theorem.- Universal Coefficient Theorems.- BV and BRST Quantization, Quantum Observables and Symmetry.- Universal Coefficient Theorem and Quantum Field Theory.- The Universal Coefficient Theorem and Black Holes.- From Grothendieck's Schemes to QCD.- Conclusions.
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