Direct measurement theory, Ito-Stratonovich theory, and weakly dissipative Kolmogorov-Arnold-Moser theory |
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Authors: | R I Bogdanov M R Bogdanov and P S Kuzin |
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Abstract: | The direct measurement theory studies linear functionals as applied to the problems of quantum mechanics in addition to considering
quadratic functionals on the space of wave functions, well established since the beginning of the 20th century. The theory
is based on the time invariance principle of an appropriate space for linear functionals. In this case, it turns out that
the second-order Schr?dinger equation is factorized: factors “respect” the effect of one of two groups, i.e., the group of
inertial gas motion or the nonlinear group. In the weakly dissipative Kolmogorov-Arnold-Moser (KAM) theory, the former group
is of extraordinary interest in connection with the formation of caustic curves which, in turn, cause the appearance of advanced
and delayed potentials, which makes it possible to estimate anew the ideas of Ito-Stratonovich in the theory of stochastic
processes. |
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