A mass gap in a quantum field theory is a positive separation between zero and the remaining operator
spectrum of the Hamiltonian, the self-adjoint linear operator generating time translations. With
the vacuum energy normalized to zero and the operator
spectrum 
contained in 
,
the theory has a mass gap if 
has no points in 
for some 
. When the nonzero operator
spectrum is nonempty, the size of the gap is
 |
The Yang-Mills existence and mass gap problem asks for such a positive gap (Jaffe and Witten).
The Yang-Mills existence and mass gap problem is one of the Millennium Prize Problems. It asks for a rigorous construction of quantum Yang-Mills theory with a positive mass gap.
