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3 results

  • 11 - Electroweak Symmetry Breaking

  • Pascal Paganini, École Polytechnique, Paris
  • Book:
    Fundamentals of Particle Physics
    Published online:
    31 August 2023
    Print publication:
    14 September 2023, pp 394-431

  • Summary

    This chapter explains how we can reconcile massive particles within a gauge symmetry. The notion of spontaneous symmetry breaking is introduced, first in a simple model and then with the gauge group of the Standard Model. The Brout–Englert–Higgs mechanism is then presented in detail. The rest of the chapter is devoted to the experimental discovery of the Higgs boson and its properties with the most up-to-date experimental measurements.

  • Integrable Systems and Torelli Theorems for the Moduli Spaces of Parabolic Bundles and Parabolic Higgs Bundles

  • Indranil Biswas, Tomás L. Gómez, Marina Logares
  • Journal:
    Canadian Journal of Mathematics / Volume 68 / Issue 3 / 01 June 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 504-520
    Print publication:
    01 June 2016
    • Article
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  • We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight systemis generic. When the genus is at least two, using this result we also prove a Torelli theoremfor the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise.

  • Higgs cohomology, p-curvature, and the Cartier isomorphism

  • Arthur Ogus
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 145-164
    Print publication:
    January 2004
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  • Let X/S be a smooth morphism of schemes in characteristic p and let $(E,\nabla)$ be a sheaf of $\mathcal{O}_{X}$-modules with integrable connection on X. We give a formula for the cohomology sheaves of the de Rham complex of $(E,\nabla)$ in terms of a Higgs complex constructed from the p-curvature of $(E,\nabla)$. This formula generalizes the classical Cartier isomorphism, with which it agrees when $(E,\nabla)$ is the constant connection.