Abstract
We propose a unified description of the known forces. We formulate a quantum relativistic spacetime as a (directed) graph of causal arrows with indefinite Hilbert metric, whose physical meaning is given. The simplest graph whose quantum relativity supports conservation of energy-momentum also supports a semidirect product of the cyclic groups2 and3 and the four-group2 2. We call these lattice degrees of freedom (permutational) twain, trine, and spin. Quantized2 2 becomes LorentzSpin(4). Gauged, the energy-momentum and spin groups lead to gravity and torsion, and twain and trine lead toSU 2 andSU 3. We infer that color is actually trine, and thez component of isospin is twain.
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Finkelstein, D., Gibbs, J.M. Quantum relativity. Int J Theor Phys 32, 1801–1813 (1993). https://doi.org/10.1007/BF00979502
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DOI: https://doi.org/10.1007/BF00979502