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-group22. We call these lattice degrees of freedom (permutational) twain, trine, and spin. Quantized22 becomes LorentzSpin(4). Gauged, the energy-momentum and spin groups lead to gravity and torsion, and twain and trine lead toSU2 andSU3. We infer that color is actually trine, and thez component of isospin is twain.
KeywordsColor Field Theory Elementary Particle Quantum Field Theory Physical Meaning
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