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Axions can be described by a relativistic field theory with a real scalar field $\phi$ whose self-interaction potential is a periodic function of $\phi$.
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P. Sikivie and Q. Yang, Bose-Einstein condensation of dark matter axions, Phys. Rev. Lett. 103
2009
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J. E. Kim and G. Carosi, Axions and the strong C P CP problem, Rev. Mod. Phys. 82
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E. Braaten, A. Mohapatra and H. Zhang, Dense axion stars, Phys. Rev. Lett. 117
2016
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