Abstract
A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products \(\mathfrak{a}_{t_1 } (F_1 ),...\;,\mathfrak{a}_{tn} (F_n )\), where \mathfraka t , t∈\(\mathbb{R}\) are time automorphisms and F j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the σ-weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.
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Kozitsky, Y. On a Theorem of Høegh-Krohn. Letters in Mathematical Physics 68, 183–193 (2004). https://doi.org/10.1023/B:MATH.0000045553.97378.3b
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DOI: https://doi.org/10.1023/B:MATH.0000045553.97378.3b