Abstract
Segal's chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in terms of which the pseudo-Hermitian realization of the Minkowski space–time is introduced and studied. The world L is based on the oscillator Lie algebra. The main idea of the DLF approach to modeling particles and interactions is that there are three Hamiltonians (the ‘Russian Troika’) to drive the evolution of a physical system.
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