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The Universal Coefficient Theorem and Quantum Field Theory

A Topological Guide for the Duality Seeker

  • Book
  • © 2017

Overview

Authors:
  1. Andrei-Tudor Patrascu

    1. Department of Physics and Astronomy, University College London Department of Physics and Astronomy, London, United Kingdom

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  • Nominated as an outstanding Ph.D. thesis by University College London, UK
  • Offers a pedagogical introduction to algebraic topology for a rapid development of basic skills
  • Provides a step-by-step approach from simple to complex, resulting in a clear and logical exposition
  • Presents original ideas to inspire new research in the quest for dualities
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction

    • Andrei-Tudor Patrascu
    Pages 1-15

  3. Elements of General Topology

    • Andrei-Tudor Patrascu
    Pages 17-30

  4. Algebraic Topology

    • Andrei-Tudor Patrascu
    Pages 31-38

  5. Homological Algebra

    • Andrei-Tudor Patrascu
    Pages 39-52

  6. Connections: Topology and Analysis

    • Andrei-Tudor Patrascu
    Pages 53-68

  7. The Atyiah Singer Index Theorem

    • Andrei-Tudor Patrascu
    Pages 69-89

  8. Universal Coefficient Theorems

    • Andrei-Tudor Patrascu
    Pages 91-106

  9. BV and BRST Quantization, Quantum Observables and Symmetry

    • Andrei-Tudor Patrascu
    Pages 107-154

  10. Universal Coefficient Theorem and Quantum Field Theory

    • Andrei-Tudor Patrascu
    Pages 155-198

  11. The Universal Coefficient Theorem and Black Holes

    • Andrei-Tudor Patrascu
    Pages 199-236

  12. From Grothendieck’s Schemes to QCD

    • Andrei-Tudor Patrascu
    Pages 237-257

  13. Conclusions

    • Andrei-Tudor Patrascu
    Pages 259-261

  14. Back Matter

    Pages 263-270
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Keywords

About this book

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 ofview, 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.


Authors and Affiliations

  • Department of Physics and Astronomy, University College London Department of Physics and Astronomy, London, United Kingdom

    Andrei-Tudor Patrascu

About the author

With a surprisingly diverse research experience covering domains from molecular spectroscopy to theoretical high energy physics and from algebraic topology and geometry to homological algebra, Andrei Patrascu seeks to understand the origin of dualities in physics. After following graduate courses at internationally renowned institutions like the Ecole Normale Superieure in Paris, Rensselaer Polytechnic Institute in Troy, NY and University College London, the author, while also working on applied physics, initiated a new research program in mathematical physics with the goal of giving a homological algebraic interpretation to some of the most important results in theoretical physics: the AdS/CFT correspondence and the ER-EPR duality. This book shows how the ideas leading to this program took shape and may become a guide towards new results of this type.
        
 


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