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 TMF, 1975, Volume 23, Number 3, Pages 355–365 (Mi tmf3846)

Separability and invariance in nonrelativstic and relativistic quantum mechanics

S. N. Sokolov

Abstract: Relation between the separability properties of the movement transformation operators $U(a)$ and the invariance and separability properties of the scattering operators $S$ is considered for the case of arbitrary (continuous) movement group $G$. The notion of $\tau_{\gamma}$-separability is introduced. It is shown that for groups $G$ possessing an invariant abelian subgroup, containing the subgroup of evolution transformations $U_t$, and, in particular, for the Galilei and Poincare groups, the invariance of the operators $S$ and their separability in time follow from the reasonably good $(\gamma >1)$ $\tau^{\gamma}$-separabiHty of the operators $U(a)$. For the Galilei and Poincare groups it is demonstrated that the separability of the operators $S$ in space is the consequence of their separability in time. It is shown that the choice of relative spatial variables, which is not unique in the relati vistic case, does not influence the properties of spatial separability.

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English version:
Theoretical and Mathematical Physics, 1975, 23:3, 567–574

Bibliographic databases:

Citation: S. N. Sokolov, “Separability and invariance in nonrelativstic and relativistic quantum mechanics”, TMF, 23:3 (1975), 355–365; Theoret. and Math. Phys., 23:3 (1975), 567–574

Citation in format AMSBIB
\Bibitem{Sok75} \by S.~N.~Sokolov \paper Separability and invariance in nonrelativstic and relativistic quantum mechanics \jour TMF \yr 1975 \vol 23 \issue 3 \pages 355--365 \mathnet{http://mi.mathnet.ru/tmf3846} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=496077} \zmath{https://zbmath.org/?q=an:0319.47008} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 23 \issue 3 \pages 567--574 \crossref{https://doi.org/10.1007/BF01041676} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. N. Sokolov, “Physical equivalence of the point and instantaneous forms of relativistic dynamics”, Theoret. and Math. Phys., 24:2 (1975), 799–803
2. G. I. Garas'ko, N. P. Klepikov, “Justification of partial-wave expansions of relativistic many-particle amplitudes”, Theoret. and Math. Phys., 31:2 (1977), 402–408
3. S. N. Sokolov, A. N. Shatnii, “Physical equivalence of the three forms of relativistic dynamics and addition of interactions in the front and instant forms”, Theoret. and Math. Phys., 37:3 (1978), 1029–1038
4. S. N. Sokolov, “Relativistic addition of direct interactions in the point form of dynamics”, Theoret. and Math. Phys., 36:2 (1978), 682–692
5. S. N. Sokolov, “Modifications of forms of relativistic dynamics related to the Pomcare transformations”, Theoret. and Math. Phys., 54:3 (1983), 224–234
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