生倒易与时空粒度
Born reciprocity and the granularity of space-time
摘要：
利用Born互易性和“非对易”相对论相空间几何解释了相对论位置和动量算符X^μ，P_v，μ，v = 0，1，2，3的Schrödinger-Robertson不等式.对于饱和薛定谔-罗伯逊不等式的状态，指出了半经典极限的类型学，其特征在于玻恩互易性的完全不变性群，即所谓的“四元”群U（3，1）xH（3，1）（酉相对论性对偶对称性U（3，1）与Weyl-Heisenberg群H（3，1）的半直积）的酉不可约表示内的轨道结构。“标量”的情况下，即相对论振荡器，和相关的多模压缩状态的例子，详细处理。在这种情况下，我们认为半经典极限对应于时空和物质以应力-能量张量和四极张量的形式分别出现，它们通常是等价的。
英文摘要：
The Schrödinger-Robertson inequality for relativistic position and momentum operators X^μ, P_ν, μ, ν= 0,1,2,3, is interpreted in terms of Born reciprocity and `non-commutative' relativistic phase space geometry. For states which saturate the Schrödinger-Robertson inequality, a typology of semiclassical limits is pointed out, characterised by the orbit structure within its unitary irreducible representations, of the full invariance group of Born reciprocity, the so-called `quaplectic' group U(3,1)xH(3,1) (the semi-direct product of the unitary relativistic dyamical symmetry U(3,1) with the Weyl-Heisenberg group H(3,1)). The example of the `scalar' case, namely the relativistic oscillator, and associated multimode squeezed states, is treated in detail. In this case,it is suggested that the semiclassical limit corresponds to the separate emergence of space-time and matter, in the form of the stress-energy tensor, and the quadrupole tensor, which are in general reciprocally equivalent.
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