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Gravitation and quadratic forms

  • Sudarshan AnanthEmail author
  • Lars Brink
  • Sucheta Majumdar
  • Mahendra Mali
  • Nabha Shah
Open Access
Regular Article - Theoretical Physics

Abstract

The light-cone Hamiltonians describing both pure (\( \mathcal{N} \) = 0) Yang-Mills and \( \mathcal{N} \) = 4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and \( \mathcal{N} \) = 8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Keywords

Classical Theories of Gravity Gauge Symmetry Supergravity Models Superspaces 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Sudarshan Ananth
    • 1
    Email author
  • Lars Brink
    • 2
    • 3
  • Sucheta Majumdar
    • 1
  • Mahendra Mali
    • 4
  • Nabha Shah
    • 1
  1. 1.Indian Institute of Science Education and ResearchPuneIndia
  2. 2.Department of PhysicsChalmers University of TechnologyGöteborgSweden
  3. 3.Institute of Advanced Studies and Department of Physics & Applied PhysicsNanyang Technological UniversitySingaporeSingapore
  4. 4.School of PhysicsIndian Institute of Science Education and ResearchTrivandrumIndia

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