Abstract
It is conjectured that the particle states of quantum mechanics are represented by functions of independent variables. These functions obey a linear differential equation which has an invariance group homomorphic to the inhomogeneous Lorentz group, thus giving a linear, Lorentz-invariant theory. Simple one-particle examples of equations which lead to a discrete particle spectrum are given, using both space–time variable, xμ, and sets of spinlike variables (pairs of complex numbers). Some of the examples have internal symmetry. No examples of realistic ’’many-body’’ particle theories are given, but we can deduce general characteristics. The differential equation must be of second or higher order to give an interaction. Products of single-particle states will be solutions of the equation and will form a complete set for widely separated particles. But products of one-particle states are not solutions of the equation for strongly interacting particles, and this permits the creation of particles. The origin of antisymmetry in such a theory is not clear.
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