Hello,
I want convert a particle’s world position to the local position of it’s emitter-object.
The bpy.types.Particle class doesn’t inherit’s the matrix_world method !
probably something like that?
mat_inv = obj.matrix_world.inverted()
local_particle_location = mat_inv @ particle.location
Thank you very much 
This helped a lot.
Is there a simple way to convert the locale_particle_location back to global location ?
yes.
global_particle_location = obj.matrix_world @ local_particle_location