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The propagator field theory revisited: a Lorentz symmetry breaking approach

arXiv - PHYS - High Energy Physics - Theory Pub Date : 2024-09-16 DOI:arxiv-2409.10313
R. Cartas-Fuentevilla, S. González-Salud, R. Bárcena-Ramos, J. Berra-Montiel
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Abstract

It is well known that the propagator for a massive scalar field is ill-defined in the coordinate space for $d\geq2$, in particular it diverges at the light-cone; we show that by using Lorentz symmetry breaking weighted measures, an infinite family of propagators can be constructed in an in\-finite\-simal strip near the light-cone, which are labeled by the weight of the measure; hence, the results will provide a finite quantum amplitude for a massive particle for propagating on the light-cone. The propagators regarded as smooth two-points functions, increase within a region smaller than the Compton wavelength, and decrease beyond that wavelength, and eventually drop off for large arguments. Although the time ordered propagators retain negative values regions for arbitrary values of the weight $s$ for the measures, the restriction $2
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重访传播者场论：打破洛伦兹对称性的方法
众所周知，大质量标量场的传播子在$d\geq2$的坐标空间中是未定义的，特别是它在光锥处发散；我们证明，通过使用打破洛伦兹对称性的加权量纲，可以在光锥附近的一个in\-finite\-simal条带中构造一个无穷的传播子系列，这些传播子用量纲的权重标记；因此，结果将为在光锥上传播的大质量粒子提供一个有限的量子振幅。传播者被视为光滑的两点函数，在小于康普顿波长的区域内增大，超过该波长后减小，对于较大的参数最终会消失。虽然时间有序传播者在度量权重 $s$ 的任意值上都保留了负值区域，但 2
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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arXiv - PHYS - High Energy Physics - Theory
arXiv - PHYS - High Energy Physics - Theory
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