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  1.  19
    The Elementary Foundations of Spacetime.James Ax - 1978 - Foundations of Physics 8 (7-8):507-546.
    This paper is an amalgam of physics and mathematical logic. It contains an elementary axiomatization of spacetime in terms of the primitive concepts of particle, signal, and transmission and reception. In the elementary language formed with these predicates we state AxiomsE, C, andU, which are naturally interpretable as basic physical properties of particles and signals. We then determine all mathematical models of this axiom system; these represent certain generalizations of the standard model. Also, the automorphism groups of the models are (...)
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  2.  28
    Group-Theoretic Treatment of the Axioms of Quantum Mechanics.James Ax - 1976 - Foundations of Physics 6 (4):371-399.
    This axiomatization is based on the observation that ifG is the group of automorphisms of the states (induced, e.g., by suitable evolutions), then we can define a spherical function by mapping each element ofG to the matrix of its transition probabilities. Starting from five physically conservative axioms, we utilize the correspondence between spherical functions and representations to apply the structure theory for compact Lie groups and their orbits in representation spaces to arrive at the standard complex Hilbert space structure of (...)
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