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2 results

  • 4 - Conservation Rules and Symmetries

  • Pascal Paganini, École Polytechnique, Paris
  • Book:
    Fundamentals of Particle Physics
    Published online:
    31 August 2023
    Print publication:
    14 September 2023, pp 101-116

  • Summary

    The notion of symmetry is essential in the determination of particle properties. It reveals quantities that are conserved in collisions or decays. It also constrains the mathematical formulation of theories. This chapter introduces these concepts and explains how the notion of symmetry is implemented in quantum mechanics. It reviews the quantities conserved in particle collisions or decays: energy-momentum and total angular momentum, and also the internal symmetries, such as parity, charge conjugation, baryon and lepton numbers.

  • 18 - The Noether Theoremand Applications

  • from Part I - General Properties of Fields; Scalars and Gauge Fields
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 165-171

  • Summary

    We study the Noether theorem, which relates a conserved charge to any global symmetry, and its applications. We define the Noether current and charge, and the general form of the Noether procedure for “gauging” the global symmetry, as well as the ambiguity of the Noether current. We apply it to translations, the Abelian U(1) symmetry, the O(N) model, and vectors in the fundamental of O(N). We define the Noether charge as an integral in terms of fields, and the transformation of the fields as the Poisson bracket of the charge with the fields.