A quantum field theory has a mass gap when the vacuum energy is separated from the rest of the spectrum by a strictly positive energy. Correlation functions then typically decay exponentially at long distance.
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The "mass gap" is a concept primarily associated with quantum field theory and particle physics, particularly in the context of the Higgs mechanism and gauge theories. It refers to the phenomenon where there is a finite difference in mass between the lightest particle (or excitation) and the next lightest one in a given theory. In simpler terms, the mass gap signifies that there is a minimum energy required to create new particles or excitations above the ground state.