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arXiv · 2312.08441

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

Paolo Creminelli·Matteo Delladio·Oliver Janssen·Alessandro Longo·Leonardo Senatore
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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.

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Paolo Creminelli, Matteo Delladio, Oliver Janssen, Alessandro Longo, Leonardo Senatore. 2023-12-13. Non-analyticity of the $S$-matrix with spontaneously broken Lorentz invariance. https://arxiv.org/abs/2312.08441

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