  The chiral plasmon modes of relativistic matter in background magnetic and
strain-induced pseudomagnetic fields are studied in detail using the consistent
chiral kinetic theory. The results reveal a number of anomalous features of
these chiral magnetic and pseudomagnetic plasmons that could be used to
identify them in experiment. In a system with nonzero electric (chiral)
chemical potential, the background magnetic (pseudomagnetic) fields not only
modify the values of the plasmon frequencies in the long-wavelength limit, but
also affect the qualitative dependence on the wave vector. Similar
modifications can be also induced by the chiral shift parameter in Weyl
materials. Interestingly, even in the absence of the chiral shift and external
fields, the chiral chemical potential alone leads to a splitting of plasmon
energies at linear order in the wave vector.
