The Doppler effect in a medium for radiation sources in motion at extreme conditions

The features of Doppler effect for radiating or absorbing quantum system in motion at parameters close to extreme condition (βn(ω) cos θ) ≈ 1 are studied. It was shown that the correct use of energy and momentum conservation laws, the dependence on radiation and absorption frequencies on (1 − βn(ω) cos θ) contains one discontinuity. The value of these frequencies has a jump discontinuity of (1 + √2). The positions of these discontinuities depend on the value (1 − βn(ω) cos θ), when normal Doppler effect transforms into abnormal.