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Lecture Notes in Physics

Resummation and Renormalization in Effective Theories of Particle Physics

Authors: Jakovác, Antal, Patkós, András

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  • First self-contained primer on this topic
  • Authored by leading specialists in the field
  • Contains detailed derivations of results
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About this book

Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure.

In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to various effective models of chiral symmetry breaking in strong interactions and the BEH-mechanism of symmetry breaking in the electroweak theory. After introducing the basics of the functional integral formulation of quantum field theories and the derivation of different variants of the equations which determine the n-point functions, the text elaborates on the formulation of the optimized perturbation theory and the large-N expansion, as applied to the solution of these underlying equations in vacuum. The optimisation aspects of the 2PI approximation is discussed. Each of them is presented as a specific reorganisation of the weak coupling perturbation theory. The dimensional reduction of high temperature field theories is discussed from the same viewpoint. The renormalization program is described for each approach in detail and particular attention is paid to the appropriate interpretation of the notion of renormalization in the presence of the Landau singularity. Finally, results which emerge from the application of these techniques to the thermodynamics of strong and electroweak interactions are reviewed in detail.

Reviews

“The lecture note deals with an effective field theory approach at finite temperatures. … The lecture note provides a first comprehensive introduction into the field for students.” (Johannes Blümlein, zbMATH 1355.81002, 2017)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-22620-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-22619-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Resummation and Renormalization in Effective Theories of Particle Physics
Authors
Series Title
Lecture Notes in Physics
Series Volume
912
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-22620-0
DOI
10.1007/978-3-319-22620-0
Softcover ISBN
978-3-319-22619-4
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XI, 223
Number of Illustrations
16 b/w illustrations, 13 illustrations in colour
Topics

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