Hamiltonian charges on light cones for linear field theories on (A)dS backgrounds

Piotr T. Chruściel (Corresponding author), Tomasz Smołka

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We analyse the Noether charges for scalar and Maxwell fields on light cones on a de Sitter, Minkowski, and anti-de Sitter backgrounds. Somewhat surprisingly, under natural asymptotic conditions all charges for the Maxwell fields on both the de Sitter and anti-de Sitter backgrounds are finite. On the other hand, one needs to renormalise the charges for the conformally-covariant scalar field when the cosmological constant does not vanish. In both cases well-defined renormalised charges, with well-defined fluxes, are obtained. Again surprisingly, a Hamiltonian analysis of a suitably rescaled scalar field leads to finite charges, without the need to renormalise. Last but not least, we indicate natural phase spaces where the Poisson algebra of charges is well defined.
Original languageEnglish
Article number102504
Number of pages51
JournalJournal of Mathematical Physics
Issue number10
Publication statusPublished - Oct 2023

Austrian Fields of Science 2012

  • 103028 Theory of relativity
  • 101006 Differential geometry
  • 103019 Mathematical physics


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