  The current form of quantum mechanics is very successful and is almost
certainly correct. It is remarkable, however, that the entire structure-from
the mass, spin and charge labels on particlelike states to antisymmetry to
broken internal symmetries to gauge transformations to the equations of
motion-is built upon concepts from group representation theory. That is, the
theory is constructed exactly as if it were a representational form of an
underlying theory. Our proposed form for the underlying theory is that it is
based on a linear equation, OF(V)=0. F is a function of some set of
independent, currently unknown variables V, with O being a linear, partial
differential operator in those variables. The operator is assumed to be
invariant under a group of transformations of the Vs, homomorphic to the direct
product of the inhomogeneous Lorentz group and the internal symmetry group. In
such a theory, a state vector, denoted by a ket with group-theoretic labels,
would represent a function of the independent variables. In addition to
explaining the group representational structure of quantum mechanics, an
underlying theory offers insight into gauge theory.
