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Resummation and Renormalization in Effective Theories of Particle Physics

  • Antal Jakovác
  • András Patkós

Part of the Lecture Notes in Physics book series (LNP, volume 912)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Antal Jakovác, András Patkós
    Pages 1-10
  3. Antal Jakovác, András Patkós
    Pages 11-47
  4. Antal Jakovác, András Patkós
    Pages 49-68
  5. Antal Jakovác, András Patkós
    Pages 69-95
  6. Antal Jakovác, András Patkós
    Pages 97-138
  7. Antal Jakovác, András Patkós
    Pages 161-187
  8. Antal Jakovác, András Patkós
    Pages 189-205
  9. Back Matter
    Pages 207-223

About this book

Introduction

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.

Keywords

2PI Approximation Chiral Phase Transitions Effective Theories in Particle Physics N-point Functions Resummation and Renormalization in Quantum Field Theories

Authors and affiliations

  • Antal Jakovác
    • 1
  • András Patkós
    • 2
  1. 1.Institute of PhysicsRoland Eötvös UniversityBudapestHungary
  2. 2.Institute of PhysicsRoland Eötvös UniversityBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22620-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-22619-4
  • Online ISBN 978-3-319-22620-0
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site