WHAT IS THE LIGHTEST EXCITED-STATE OF THE STRONGLY SELFCOUPLED HIGGS FIELD

We argue for the existence of an upper bound m on the Higgs mass at w hich the lowest excited state of the Higgs field ceases to be the conv entional plane wave. An explicit construction of an alternative nonper turbative state is discussed. This excitation is spatially localized. The field fluctuations inside the localization region are large. The e nergy of the excitation is smaller than the mass of the plane wave sta te m at m > m. An approximate value of m* is found to be m* approxima te to 4.75 times the vacuum expectation value. This is an upper bound at the tree level.