We extend a recent approach to Deformed Special Relativity based on deformeddispersion laws, entailing modified Lorentz transformations and, at the sametime, noncommutative geometry and intrinsically discrete spacetime. In so doingwe obtain the explicit form of the modified Lorentz transformations for aspecial class of modified momentum-energy relations often found in literatureand arising from elementary particle physics. Actually, our theory looks as avery simple and natural extension of special relativity to include a momentumcut-off at the Planck scale. In particular, the new Lorentz transformations doimply that for high boost speed ($V \sim c$) the deformed Lorentz factor doesnot diverge as in ordinary relativity, but results to be upperly bounded by alarge finite value of the order of the ratio between the Planck mass and theparticle mass. We also predict that a generic boost leaves unchanged Planckenergy and momentum, which result invariant with respect to any referenceframe.
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机译：我们基于变形分散定律扩展了最近的变形相对论方法，需要修改的洛伦兹变换，同时还需要非对易几何和本质上离散的时空。这样做，我们获得了在文献中经常发现的，源自基本粒子物理学的特殊类的动量-能量关系的特殊形式的修正的洛伦兹变换的显式形式。实际上，我们的理论看起来像是狭义相对论的每一个简单自然的扩展，包括了普朗克尺度的动量截止。特别是，新的洛伦兹变换令人困惑地认为，对于高提升速度（$ V \ sim c $），变形的洛伦兹因子不会像普通相对论那样发散，但会受到较大的有限值比率的上界限制，普朗克质量和粒子质量。我们还预测，通用助推器将使Planckenergy和动量保持不变，这将导致相对于任何参考系不变。
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