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51 results

Page 1 of 3

Uncovering Quantum Field Theory and the Standard Model
  • From Fundamental Concepts to Dynamical Mechanisms
  • Wolfgang Bietenholz, Uwe-Jens Wiese
  • Published online:
    06 February 2025
    Print publication:
    02 January 2025
  • This textbook provides an accessible introduction to quantum field theory and the Standard Model of particle physics. It adopts a distinctive pedagogical approach with clear, intuitive explanations to complement the mathematical exposition. The book begins with basic principles of quantum field theory, relating them to quantum mechanics, classical field theory, and statistical mechanics, before building towards a detailed description of the Standard Model. Its concepts and components are introduced step by step, and their dynamical roles and interactions are gradually established. Advanced topics of current research are woven into the discussion and key chapters address physics beyond the Standard Model, covering subjects such as axions, technicolor, and Grand Unified Theories. This book is ideal for graduate courses and as a reference and inspiration for experienced researchers. Additional material is provided in appendices, while numerous end-of-chapter problems and quick questions reinforce the understanding and prepare students for their own research.

  • 20 - U(1)A-Problem

  • from Part III - Strong Interaction
  • Wolfgang Bietenholz, Universidad Nacional Autónoma de México, Uwe-Jens Wiese, Universität Bern, Switzerland
  • Book:
    Uncovering Quantum Field Theory and the Standard Model
    Published online:
    06 February 2025
    Print publication:
    02 January 2025, pp 442-449

  • Summary

    This chapter reviews the solution to the U(1)A-problem, from a quantitative perspective. We discuss the ‘t Hooft large-Nc limit of QCD, which removes the axial anomaly, and its reappearance under 1/ Nc corrections. This provides mass to the η’ meson, which is related to the topological susceptibility by the Witten–Veneziano formula. This susceptibility is now well-defined on the lattice, based on the index theorem. It has a controlled continuum limit, which substantiates the Witten–Veneziano formula.

  • 5 - Renormalization Group

  • from Part I - Quantum Field Theory
  • Wolfgang Bietenholz, Universidad Nacional Autónoma de México, Uwe-Jens Wiese, Universität Bern, Switzerland
  • Book:
    Uncovering Quantum Field Theory and the Standard Model
    Published online:
    06 February 2025
    Print publication:
    02 January 2025, pp 87-106

  • Summary

    This chapter deals with the renormalization group in Wilson’s spirit. General concepts, like fixed points, are illustrated with examples, such as block-variable transformations, perfect lattice actions, the Wilson–Fisher fixed points, the Callan–Symanzik equation, and various scenarios for running couplings.

Page 1 of 3