奇数维空间的同步辐射
Synchrotron radiation in odd dimensions
摘要：
在奇维时空中，无质量波动方程的延迟解不仅在光锥上有支持，而且在光锥内部也有支持，同时，一个自由的无质量场应该以光速传播。这两个特征之间的明显矛盾可以通过波区中场的发射部分取决于直到真时的延迟时刻的运动历史这一事实来解决。结果表明，在超相对论速度的圆周运动的情况下，辐射振幅的主要贡献是由延迟时间之前的一个小的时间间隔的适当的时间，从而有效地本地化的尾部项。我们得到了$D$维中标量同步辐射的一个试探公式：$P =g^2(ω_0γ^2/\sqrt{3})^{D-2}$，并在$D=3,\,4,\,5$中得到了明确的验证.
英文摘要：
In odd space-time dimensions, the retarded solution of the massless wave equation has support not only on the light cone, but also inside it. At the same time, a free massless field should propagate at the speed of light. The apparent contradiction of these two features is resolved by the fact that the emitted part of the field in the wave zone depends on the history of motion up to the retarded moment of proper time. It is shown that in the case of circular motion with ultrarelativistic velocity, the main contribution to the radiation amplitude is made by a small interval of proper time preceding the retarded time, and thus the tail term is effectively localized. We obtain a tentative formula for scalar synchrotron radiation in $D$ dimensions: $P =g^2(ω_0γ^2/\sqrt{3})^{D-2}$, which is explicitly verified in $D=3,\,4,\,5$.
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