arXiv 2602.169712026-02hep-th

符号-戈尔登谱质量来自非线性傅里叶模态混合

Signum-Gordon spectral mass from nonlinear Fourier mode mixing

Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）

João S. Streibel, Pawel Klimas

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AI总结：

研究符号-戈尔登模型中谱质量的产生，通过分析单色波列车的演化，发现两种动态 regime，揭示非线性傅里叶模态混合机制，展示模型有效模仿有质量理论，实现非解析标量模型的质量量化。

摘要：

我们研究符号-戈尔登模型中谱质量的出现，这是一种非解析、V形势的非线性场论，其中标准微扰质量定义不适用。通过分析单色波列车的演化，我们识别出两种由波幅与波数关系决定的动态 regime。在非线性 regime 中，模型表现出非线性傅里叶模态混合，其中势的非解析性作为源，填充高阶谐波。使用两种互补的数值方法——跟踪初始波数的频率分布和测量边界信号的空间响应——我们构建了能量-动量空间的完整色散图。我们的结果表明，符号-戈尔登场有效地模仿有质量理论。具体而言，我们展示特定初始波幅诱导单位谱质量，完美匹配 massive Klein-Gordon 方程的行为，为非解析标量模型的质量量化提供稳健框架。

英文摘要：

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.

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