关于狭义相对论的芬斯勒推广
On Finslerian extension of special relativity
摘要：
我们证明了Robb-Geroch的相对论区间的定义承认一个简单的和相当自然的推广导致芬斯勒扩展的狭义相对论。另一个理由，这样一个扩展可以追溯到工作的Lalan和Alway，最后，是把一个坚实的基础和系统的研究Bogoslovsky的名义下“特殊相对论理论的局部各向异性时空”。这个时空的等距群$\mathrm{DISIM}_b(2)$，是科恩和希豪的狭义相对论对称群$\mathrm{ISIM(2)}$的变形。因此，变形参数b可以被视为表征庞加莱群变形为德西特（反德西特）群的宇宙学常数的模拟。本文上下文中芬斯勒扩张的简单性和自然性增加了以下论点的分量：应该仔细考虑$b$非零值的可能性。
英文摘要：
We demonstrate that Robb-Geroch's definition of a relativistic interval admits a simple and fairly natural generalization leading to a Finsler extension of special relativity. Another justification for such an extension goes back to the works of Lalan and Alway and, finally, was put on a solid basis and systematically investigated by Bogoslovsky under the name "Special-relativistic theory of locally anisotropic space-time". The isometry group of this space-time, $\mathrm{DISIM}_b(2)$, is a deformation of the Cohen and Glashow's very special relativity symmetry group $\mathrm{ISIM(2)}$. Thus, the deformation parameter b can be regarded as an analog of the cosmological constant characterizing the deformation of the Poincare group into the de Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian extension in the context of this article adds weight to the argument that the possibility of a nonzero value of $b$ should be carefully considered.
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