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By David Ginsburg

Treats sure difficulties and strategies of theoretical physics and astrophysics that are linked to microscopic and macroscopic electrodynamics and fabric in regards to the concept of transition radiation and transition scattering.

"'An very good resource of knowledge and insights on those topics...potentially very priceless either for study scholars physicists.'." -- Professor C.H. Llewellyn Smith of FRS, Chairman of Physics, Clarendon Laboratory, Oxford collage, England

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7)). The reverse conclusion would, however, be incorrect. e. 9) was satisfied). 9) that is satisfied. Indeed, differentiation of the equation of motion with respect to s, du; e pik i -=:w = - ds mc 2 Uk, shows that dwi ds e pik -=- mc 2 wk ' dwi 1d ; _ e ik _ W· = - - (w W·) - - F wk W· - 0 2 ' ' ds ' 2 ds ' mc - 40 THEORETICAL PHYSICS AND ASTROPHYSICS since the electromagnetic field tensor F 1k is antisymmetric. We have taken into account not only the constancy of the field (its independence of time) but also its uniformity, and we have used in the equations of motion the field at the point "occupied" by the charge (then F 1k = F 1k(t, r(t)) (we can ignore the derivative of F 1k with respect to s, as we have done above, only if F 1k is independent of both t and r).

F. 2e 2 ... 1) where f = 2e 2 r/3c 3 is the radiation reaction force (the radiation force or the radiative friction force), and F0 is an external force, which has the form F0 = eE0 + ! 2) if its nature is purely electromagnetic. g. 1) without any additional assumptions. 1) can therefore ·be directly applicable to the relativistic case (see Chapter 4). 1) is not applicable in a straightforward manner. 4) where we have assumed (v/e)H0 « E0 for the sake of simplicity. 3) is equivalent to the conditions • 2 I.

We have used here the notation introduced in [2]. Then the four-velocity is v2)-112} v2)-112 v( 1-{( . dx; 0 ,u)= , ,1--=u'=(u 2 c2 c c ds and v2)112 dt, u1u; = u~ - u2 = 1, ds = c( 1 - c2 (v·v)v } v v·v ; du; { w = ds = c3(1 - v2/c2)2' c2(1 - v2/c2) + c4(1 - v2;c2)2 ' where Ii= dv/dt. We can readily obtain (ai) 2 - (c- 1 v x ai) 2 c4(1 - v2/c2)3 . 6) allows us to treat it in any inertial frame of reference. 5) is valid for any R in the frame of reference in which v = 0, and we can therefore calculate the emitted energy and establish the presence of radiation not only in the wave zone but in the vicinity of the charge too.

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