this afternoon while i was working in my electronics room, suddenly it flashed into my mind as a recollection how the Planck's constant, a quantum mechanical constant being used as a conversion factor for the mass of the Klein-Gordon scalar along with speed of light c, see the classical action (10), this exercise in the classical context but what pops out are solutions specially the spatial modes that somewhat correspond to quantized frequencies in the imaginary time but i urge you to do the exercise yourself this is just an exercise! still an ongoing one among others... btw, watch out for the typos, there might be some that are intentional
https://foxtrotpaparomeo.wordpress.com/2022/11/08/the-klein-gordon-field-in-two-dimensional-rindler-space-time-8november2022/