Saved in:
Bibliographic Details
Main Authors: Streibel, João S., Klimas, Pawel
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.16971
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917411164258304
author Streibel, João S.
Klimas, Pawel
author_facet Streibel, João S.
Klimas, Pawel
contents We investigate the emergence of a spectral mass in the signum-Gordon model, a nonlinear field theory characterized by a non-analytic, V-shaped potential where standard perturbative mass definitions are inapplicable. By analyzing the evolution of monochromatic wave trains, we identify two distinct dynamical regimes governed by the relationship between the wave's amplitude and its wavenumber. In the nonlinear regime, the model exhibits nonlinear Fourier mode mixing, where the potential's lack of analyticity acts as a source that populates higher-order harmonics. Using two complementary numerical methods -- tracking frequency distributions from initial wavenumbers and measuring spatial responses to boundary signals -- we construct comprehensive dispersion maps in energy-momentum space. Our results demonstrate that the signum-Gordon field effectively mimics a massive theory. Specifically, we show that a particular initial wave amplitude induces a spectral mass of unity, perfectly matching the behavior of the massive Klein-Gordon equation and providing a robust framework for quantifying mass in non-analytic scalar models.
format Preprint
id arxiv_https___arxiv_org_abs_2602_16971
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Signum-Gordon spectral mass from nonlinear Fourier mode mixing
Streibel, João S.
Klimas, Pawel
High Energy Physics - Theory
We investigate the emergence of a spectral mass in the signum-Gordon model, a nonlinear field theory characterized by a non-analytic, V-shaped potential where standard perturbative mass definitions are inapplicable. By analyzing the evolution of monochromatic wave trains, we identify two distinct dynamical regimes governed by the relationship between the wave's amplitude and its wavenumber. In the nonlinear regime, the model exhibits nonlinear Fourier mode mixing, where the potential's lack of analyticity acts as a source that populates higher-order harmonics. Using two complementary numerical methods -- tracking frequency distributions from initial wavenumbers and measuring spatial responses to boundary signals -- we construct comprehensive dispersion maps in energy-momentum space. Our results demonstrate that the signum-Gordon field effectively mimics a massive theory. Specifically, we show that a particular initial wave amplitude induces a spectral mass of unity, perfectly matching the behavior of the massive Klein-Gordon equation and providing a robust framework for quantifying mass in non-analytic scalar models.
title Signum-Gordon spectral mass from nonlinear Fourier mode mixing
topic High Energy Physics - Theory
url https://arxiv.org/abs/2602.16971