Summary
Even though the unitary representations of the pseudo-orthogonal groups O(p, q) (that is, of the groups of transformations that leave the form\(x_1^2 + x_2^2 + ... + x_p^2 - x_{p + 1}^2 - ... - x_{p + q}^2\) invariant) are known in principle,* the physical interpretation of the most important of them, of the ordinary de Sitter group O(4, 1), has not been adequately elucidated. The principal purpose of the present chapter is to contribute toward such elucidation, in particular, toward the understanding of how the positive nature of the energy can be incorporated into the interpretation. No attempt will be made at full generality nor at complete mathematical rigor. Nevertheless, a few problems of mathematical pathology will have to be discussed.
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Philips, T.O., Wigner, E.P. (1997). de Sitter Space and Positive Energy. In: Wightman, A.S. (eds) Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. The Scientific Papers, vol A / 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09203-3_23
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