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A lower limit to the amount of energy that a particle can have is a property of a particle with a mass.An object may have any amount of kinetic energy, the amount getting smaller as the body slows toward rest. At this point the particle has its mini-mum energy; the amount of which, E, would then correspond to a mass m given by Einstein’s famous equation $E=mc^2$. For a massless body, the minimum energy in principle can be zero. From "The Infinity Puzzle", by Frank Close
See: The Concept of Mass by Okun
QFT is not a theory which ”creates” masses of model-defining fields. The masses of those free fields which define the first order interaction density) are, together with the coupling strengths, free parameters5 . The only ”dynamic” masses are those of bound states created by acting with interacting composite fields on the vacuum state but unfortunately there is no perturbative methods which describes bound states. spacehttps://arxiv.org/pdf/1612.00003.pdf