DOI: https://doi.org/10.30970/jps.18.2003
ON THE CHRAPLYVY TRANSFORMATION AND SOME FEATURES OF ITS APPLICATION FOR HIGHER-ORDER EXPANSIONS. II
Alexei Turovsky
Bogolyubov Institute for Theoretical Physics, NAS of Ukraine,
Kyiv, UA-03680, Ukraine
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Journal of Physical Studies 18(2/3), Article 2003 [5 pages] (2014)
DOI: https://doi.org/10.30970/jps.18.2003 ON THE CHRAPLYVY TRANSFORMATION AND SOME FEATURES OF ITS APPLICATION FOR HIGHER-ORDER EXPANSIONS. IIAlexei Turovsky
Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, |
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Using a sequence of canonical transformations with the generating functions for the case of particles with arbitrary masses, valid for particles of equal masses as well, the transformation of the relativistic two-body Hamiltonian containing even-even, even-odd, odd-even, and odd-odd terms into an even-even form is carried out up to the order $1/c^4$. It is shown that, similarly to the transformation based on the set of generators excluding the case of equal masses of the particles, the final form of the obtained approximate Hamiltonian is not uniquely defined; namely, it depends on the order of application of the initial generators in the procedure, and can involve certain extra terms, which are eliminated with an additional unitary transformation.
PACS number(s): 03.65.Pm, 03.65.Ca, 02.30.Mv, 31.30.jy