arXiv 1201.57552012-01hep-thgr-qchep-ph

广义相对论中的定域超光速子

Localized Propagating Tachyons in Extended Relativity Theories

Matej Pavšič

备注：: 28 pages, 3 figures; A subsection on a generalization of the tachyonic Dirac equation by Chodos et al. has been included

摘要：

我们研究了在适当扩展的相对论中局部传播快子场的可能性。一个可能的扩展是包括超光速变换和参考系。这就导致了复杂的四维时空，或实的8D时空M_{4,4}。在M_{4,4}中的质量壳约束在第一次量子化之后变成超双曲Klein-Gordon方程。这类方程的柯西问题是不好定的，因为在M_{4,4}的7 D超曲面上不可能自由地指定初始数据。我们明确地表明，这是可能的，它是在一个类似空间的4-表面的缓子，和一个类似时间的4-表面的快子。但是，慢子场向四个类时方向的演化，或者快子场向四个类空方向的“演化”，并不是唯一确定的。我们认为，这也许不是那么糟糕，因为在量子场论中（在第二次量子化之后），场的经典轨迹无论如何都是不确定的，因此，如果它们在第一次量子化理论中没有完全确定，那也没关系。相对论的下一个可能的扩展是考虑16维克利福德空间，C，一个空间的元素是定向的r-体积，r= 0，1，2，3，4的真实四维时空。然后，演化参数可以与额外的光锥坐标相关联，例如，用标量坐标与伪标量坐标之和，初始数据可以在类光超曲面上给出，在这种情况下，柯西问题是适定的。这个过程使我们的Stueckelberg理论，其中包含本地化的传播快子在4D时空。

英文摘要：

We examine the possibility of localized propagating tachyonic fields within a properly extended relativity. A possible extension is to include superluminal transformations and reference frames. This leads to complex 4D spacetime, or real 8D spacetime M_{4,4}. The mass shell constraint in M_{4,4} becomes, after first quantization, the ultrahyperbolic Klein-Gordon equation. The Cauchy problem for such equation is not well posed, because it is not possible to freely specify initial data on a 7D hypersurface of M_{4,4}. We explicitly demonstrate that it is possible to do it on a space-like 4-surface for bradyons, and on a time-like 4-surface for tachyons. But then the evolution of a bradyonic field into the four time-like directions, or the "evolution" of a tachyonic field into the four space-like directions, is not uniquely determined. We argue that this is perhaps no so bad, because in quantum field theory (after second quantization) the classical trajectories of fields are not determined anyway, and so it does not matter, if they are not completely determined already in the first quantized theory. A next possible extension of relativity is to consider 16D Clifford space, C, a space whose elements are oriented r-volumes, r=0,1,2,3,4 of real 4D spacetime. Then the evolution parameter can be associated with an extra light-cone coordinate, e.g., with the sum of the scalar and the pseudoscalar coordinate, and initial data can be given on a light-like hypersurface, in which case the Cauchy problem is well posed. This procedure brings us to the Stueckelberg theory which contains localized propagating tachyons in 4D spacetime.

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英文摘要：

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