An old thread (https://www.physicsforums.com/threads/state-observable-duality-john-baez-series.451101/) triggered a lively debate on whether complex functions are necessary for quantum theory or real functions (but not pairs of real functions) can be sufficient for it. I argued that one real function is generally enough to describe a charged scalar field in electromagnetic field (in the Klein-Gordon equation) and a charged spinor field in electromagnetic field (in the Dirac equation). I have found out recently (https://arxiv.org/abs/1811.02441) that one real function is also generally enough to describe a spinor field in Yang-Mills field (in the Dirac equation in Yang-Mills field), although such spinor field contains [itex]4n[/itex] complex components (for SU([itex]n[/itex]) Yang-Mills field).(adsbygoogle = window.adsbygoogle || []).push({});

Abstract: "Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function, and the remaining component can be made real by a gauge transformation. This work extends the result to the case of the Dirac equation in the Yang-Mills field."

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# I Real function instead of spinor field in Yang-Mills field

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