对N.B.Bruno、G.Amelino-Camelia和J.Kowalski-Glikman的论文“Deformed Boost Transformations that saturate at the Planck Scale”的评论
A comment on the paper "Deformed Boost Transformations that saturate at the Planck Scale" by N.B.Bruno,G.Amelino-Camelia, and J.Kowalski-Glikman
摘要：
本文给出了[1]中给出的色散关系和动量-能量四维矢量$p_i,p_0$表达式的另一种（简化）推导方法。事实证明，以一种相当“普通”的方式，人们不仅可以在一个笔划中获得上述关系，而且还可以获得$ω-k_i$空间中的正确色散关系，与无质量粒子的速度值相一致。这是通过考虑$ω-k_i$ -空间的标准洛伦兹代数来实现的。讨论了有限长度尺度下时间导数选择的非唯一性。结果表明，这种非唯一性不影响$ω-k_i$ -空间中的色散关系。尽管取决于时间导数的定义的选择，在$p-p_0$空间中导致不同的色散关系。
英文摘要：
An alternative (simplified) derivation of the dispersion relation and the expressions for the momentum-energy 4-vector $p_i,p_0$ given initially in [1] is provided. It has turned out that in a rather "pedestrian" manner one can obtain in one stroke not only the above relations but also the correct dispersion relation in $ω-k_i$ space, consistent with the value of a velocity of a massless particle. This is achieved by considering the standard Lorentz algebra for $ω-k_i$-space. A non-uniqueness of the choice of the time-derivative in the presence of the finite length scale is discussed. It is shown that such non-uniqueness does not affect the dispersion relation in $ω-k_i$-space. albeit results in different dispersion relations in $p-p_0$-space depending on the choice of the definition of the time derivative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
