Differences between translation-invariant and broken-symmetry bipolaron theories are analyzed in detail. It is shown that the Bogolyubov-Tyablikov canonical transformation allows collective coordinates to be introduced in a regular way for two particles in a quantum field and that for the case of the bipolaron the resulting electron-electron interaction in a phonon field depends on the electron coordinate difference alone. Predictions using a revised solution of the nonlinear differential equations for a bipolaron are given. It is shown that solving bipolaron equations numerically reduces the total bipolaron energies compared to known variational results.

PACS: 71.38.+i DOI: 10.1070/PU1998v041n04ABEH000385 URL: https://ufn.ru/en/articles/1998/4/d/ 000074653300004 Citation: Lakhno V D "Translation invariance and the problem of the bipolaron" Phys. Usp. 41 403–406 (1998) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Лахно В Д «Трансляционная инвариантность и проблема биполярона» УФН 168 465–469 (1998); DOI: 10.3367/UFNr.0168.199804d.0465