Can the Higgs Field Explain Relativistic Momentum and Energy?

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Can the theoretical Higgs Field be used as the “cause” of relativistic momentum or relativistic kinetic energy of a moving body?
 
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No, the special relativistic relations between energy, momentum, and mass are more fundamental than that. The Higgs mechanism relates to just one specific class of theories within the broader framework of relativistic quantum field theory. Here the "relativistic" means "obeys special relativity."