Abstract
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: $P =g^2(\omega_0\gamma^2/\sqrt{3})^{D-2}$, which is explicitly verified in $D=3,\,4,\,5$.
Highlights
Over the past two decades, interest has arisen in the theory of radiation in space-time dimensions other than four
More than a hundred years ago, Ehrenfest [4] called the features of radiation in four-dimensional electrodynamics a unique manifestation of the dimensionality of spacetime, so different are the physical effects and the theoretical description of radiation in other dimensions
General features of wave propagation in arbitrary dimensions were discussed in the classical collections of mathematical physics, such as Courant and Hilbert [5], lectures of Hadamard [6], the book by Ivanenko and Sokolov [7]
Summary
Over the past two decades, interest has arisen in the theory of radiation in space-time dimensions other than four This was due to the emergence of theories with large extra dimensions [1], the development of a holographic approach to the description of quark-gluon plasma [2,3], the beginning of gravitational-wave astronomy, and other reasons. Radiation is the main classical and quantum process of the interaction of charged particles with massless fields, which are basic ingredients of a number of theories It seems to be of primary importance to study the general laws of radiation in space-times other than four-dimensional. Our results were double checked by calculating the spectral distribution of radiation, which is insensitive to whether the dimension is even or odd We expect they can be tested within the framework of an effective field theory approach developed in Refs. In the last section we briefly formulate our results and discuss relation to other work
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