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Modified commutators vs. modified operators in a quantum gravity minimal length scale

机译:修改的换向器与修改的运算符以量子重力最小长度尺度

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Ideas about quantum gravity often postulate that at some high energy/momentum scale there will be a fixed, minimal length. Such a minimal length can be phenomenologically investigated by modifying the usual Heisenberg Uncertainty Relation-ship, ΔxΔp≥h/2, which in turn means modifying the commutator between position and momentum operators, which in turn means means modifying these operators. We show that it is the modification of the position and momentum operators which is the key determining factor in the existence (or not) of a minimal length scale. By focusing on the primacy of the role of the operators we also show that one can avoid the implications from the observations of certain short gamma ray bursts which in certain cases seem to push a minimal length scale above the Planck scale.
机译:关于量子重力的想法经常假设在一些高能量/动量尺度下,将存在固定,最小的长度。 这种最小长度可以通过修改通常的Heisenberg不确定性关系 - ΔxΔp≥h/ 2来对这种最小程度的调查,这又意味着修改位置和动量操作员之间的换向器,这又意味着修改这些操作员。 我们表明它是修改的位置和动量运算符,其是最小长度的存在(与否)的关键确定因子。 通过专注于运营商的角色的首要,我们还表明,在某些情况下,可以避免某些短伽马射线突发的观察的影响似乎在普朗克规模上方推出最小的长度尺度。

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