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4735 results in Particle Physics and Nuclear Physics

Page 182 of 237

  • 58 - More on spectral sum rules

  • from Part X - QCD spectral sum rules
  • Stephan Narison, Université de Montpellier II
  • Book:
    QCD as a Theory of Hadrons
    Published online:
    03 February 2010
    Print publication:
    02 February 2004, pp 696-698

  • Summary

    QSSR have wider applications and can also be applied to theories other than QCD as it is based on first principles of analyticity and duality.

    Some other applications in QCD

    Some other applications of QSSR have been already reviewed in details in the book [3], which we list below:

    • Baryons at large Nc.

    • String tension from Wilson loops.

    • Relation between lattice correlators and chiral symmetry breaking in the continuum limit.

    • Two-dimensional QCD.

    Electroweak models with dynamic symmetry breaking

    QSSR has been also extended in order to give dynamic constraints on fermions and W, Z bosons assumed to be bound states of preons (haplons) where the structures may manifest at the TeV scale. The analysis has been done by assuming that at that scale, one can have a strong interaction theory of preons that is closely analogous to QCD describing the electroweak interactions, with the exception that one has to be careful on the chirality of the theories:

    • In [868] and [869], (reviewed in [870]), QSSR (Laplace and FESR) have been used in order to test the consistency of the compositeness assumption for the W and Z bosons and its spin zero partners, in the haplon model proposed by Fritzsch and Mandelbaum [871], leading to a duality constraint between the boson masses and couplings with the continuum threshold (compositeness scale).

    • […]

  • 5 - Lagrangian and gauge invariance

  • from Part II - QCD gauge theory
  • Stephan Narison, Université de Montpellier II
  • Book:
    QCD as a Theory of Hadrons
    Published online:
    03 February 2010
    Print publication:
    02 February 2004, pp 57-62

  • Summary

    Introduction

    After Einstein's identification of the invariance group of space and time in 1905, symmetry principles received an enthusiastic welcome in physics, with the hope that these principles could express the simplicity of nature in its deepest level. Since 1927 [99,100], it has been recognized that Quantum ElectroDynamics (QED) has a local symmetry under the transformations in which the electron field has a phase change that can vary point to point in space–time, and the electromagnetic vector potential undergoes a corresponding transformation. This kind of transformation is called a U(1) gauge symmetry due to the fact that a simple phase change can be thought as a multiplication by a 1 × 1 unitary matrix. Largely motivated by the challenge of giving a field-theoretical framework to the concept of isospin invariance, Yang and Mills [101] in 1954 extended the idea of QED to the SU(2) group of symmetry. However, it appears here that the symmetry would have to be approximate because gauge invariance requires massless vector bosons like the photon, and it seems obvious that strong interactions of pions were not mediated by massless but by the massive ρ mesons. In 1961, there was the idea of dynamic breaking, i.e., the Hamiltonian and commutation relations of a quantum theory could possess an exact symmetry and the symmetry of the Hamiltonian might not turn to be a symmetry of the vacuum.

Page 182 of 237