ENGLISH

The Universal Coefficient Theorem and Quantum Field Theory: A Topological Guide for the Duality Seeker

By Andrei-Tudor Patrascu

Book information

Publisher
Springer
Year
2017
ISBN
3319461427, 978-3-319-46142-7, 978-3-319-46143-4, 3319461435
Language
english
Format
PDF
Filesize
2 MB (2166156 bytes)
Series
Springer Theses Recognizing Outstanding Ph.D. Research
Edition
1st ed.
Pages
270\279
Library
kolxoz
Time added
2017-10-15 16:00:00
Mathematical physics;Algebraic topology;Quantum fi

Description

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. Front Matter....Pages i-xvi Introduction....Pages 1-15 Elements of General Topology....Pages 17-30 Algebraic Topology....Pages 31-38 Homological Algebra....Pages 39-52 Connections: Topology and Analysis....Pages 53-68 The Atyiah Singer Index Theorem....Pages 69-89 Universal Coefficient Theorems....Pages 91-106 BV and BRST Quantization, Quantum Observables and Symmetry....Pages 107-154 Universal Coefficient Theorem and Quantum Field Theory....Pages 155-198 The Universal Coefficient Theorem and Black Holes....Pages 199-236 From Grothendieck’s Schemes to QCD....Pages 237-257 Conclusions....Pages 259-261 Back Matter....Pages 263-270

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