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abstract: 'We obtain a system of exact solutions of the Dirac equation for an electron moving in a constant homogeneous external magnetic field with account of its vacuum magnetic moment and assumed Lorentz invariance violation in the minimal CPT-odd form in the framework of the Standard Model Extension. Using these solutions, characteristics of the particle synchrotron radiation are calculated, and possible observable effects caused by the Lorentz non-invariant interaction are described. We demonstrate that the angular distribution of the radiation has specific asymmetry, which can be explained as a consequence of non-conservation of transversal electron polarization in the presence of a background Lorentz non-invariant condensate field.'
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**Synchrotron Radiation in the Standard Model Extension**

I. E. Frolov, V. Ch. Zhukovsky,\
[ *Faculty of Physics, Department of Theoretical Physics,\
Moscow State University, 119899, Moscow, Russia.* ]{}

Introduction {#intro}
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According to the modern viewpoint, the standard quantum field theory model of elementary particles is a low-energy approximation of a certain more fundamental theory which unites in some way all known types of physical interactions together. As a consequence there must exist (and, in spite of their extreme subtleness, be observable) specific effects, which are not inherent in the standard model 