IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i6p890-d1358899.html
   My bibliography  Save this article

Dirac Geometric Approach for the Unimodular Holst Action

Author

Listed:
  • Bogar Díaz

    (Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México 04510, Mexico
    Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
    Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain)

  • Eduardo J. S. Villaseñor

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
    Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán (UC3M), Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain)

  • Diana Zomeño Salas

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain)

Abstract

We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional elements, such as parametrization, complex fields, or considering the Barbero–Immirzi parameter as imaginary. We show that, by using a geometric implementation of the Dirac algorithm, a comprehensive analysis of the theory can be conducted without relying on these additional ingredients. The resulting theory reproduces the behavior of metric unimodular gravity.

Suggested Citation

  • Bogar Díaz & Eduardo J. S. Villaseñor & Diana Zomeño Salas, 2024. "Dirac Geometric Approach for the Unimodular Holst Action," Mathematics, MDPI, vol. 12(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:890-:d:1358899
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/6/890/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/6/890/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Van Der Bij, J.J. & Van Dam, H. & Ng, Yee Jack, 1982. "The exchange of massless spin-two particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 307-320.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:890-:d:1358899. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.