Abstract
A theory of quantum mechanics underlying the current theory is proposed. Every state—including the vacuum—must satisfy the linear equationOΨ=0. Ψ is a sum of products of spin-1/2 kets.O is a linear operator invariant under the inhomogeneous Lorentz group and the unitary group (U(n). It is modelled after the integral of the Lagrangian density in quantum field theory, and is expressed in terms of spin-1/2 kets and bras. Interaction-mediating vector bosons enter as collective oscillations of the vacuum. The direct four-fermion interaction inO can be re-expressed as a fermion-boson interaction. The form of the boson creation, operators is derived from gauge transformation arguments. The additional assumption of a very small structure constant for the vacuum leads to an understanding of the ∂θ/∂x μ term which is added to the boson potential by a gauge transformation. The possible forms and effects of spontaneous symmetry breaking of the vacuum are discussed.
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