Journal of High Energy Physics (Jun 2024)

Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance

  • Paolo Creminelli,
  • Matteo Delladio,
  • Oliver Janssen,
  • Alessandro Longo,
  • Leonardo Senatore

DOI
https://doi.org/10.1007/JHEP06(2024)201
Journal volume & issue
Vol. 2024, no. 6
pp. 1 – 28

Abstract

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Abstract We study the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

Keywords