article published yes Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department NSERC Postdoctoral fellowship project We review recent progress towards a rigorous understanding of the Bogoliubov approximation for bosonic quantum many-body systems. We focus, in particular, on the excitation spectrum of a Bose gas in the mean-field (Hartree) limit. A list of open problems will be discussed at the end. https://research-explorer.ista.ac.at/download/1821/5172/IST-2016-532-v1+1_J._Mathematical_Phys._2014_Seiringer.pdf application/pdfno American Institute of Physics2014 eng 00034117460001010.1063/1.4881536 557 Seiringer R. 2014. Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. Journal of Mathematical Physics. 55(7), 1.4881536. Seiringer, Robert. “Bose Gases, Bose-Einstein Condensation, and the Bogoliubov Approximation.” <i>Journal of Mathematical Physics</i>. American Institute of Physics, 2014. <a href="https://doi.org/10.1063/1.4881536">https://doi.org/10.1063/1.4881536</a>. Seiringer, R. (2014). Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. <i>Journal of Mathematical Physics</i>. American Institute of Physics. <a href="https://doi.org/10.1063/1.4881536">https://doi.org/10.1063/1.4881536</a> R. Seiringer, “Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation,” <i>Journal of Mathematical Physics</i>, vol. 55, no. 7. American Institute of Physics, 2014. Seiringer R. Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. <i>Journal of Mathematical Physics</i>. 2014;55(7). doi:<a href="https://doi.org/10.1063/1.4881536">10.1063/1.4881536</a> Seiringer, Robert. “Bose Gases, Bose-Einstein Condensation, and the Bogoliubov Approximation.” <i>Journal of Mathematical Physics</i>, vol. 55, no. 7, 1.4881536, American Institute of Physics, 2014, doi:<a href="https://doi.org/10.1063/1.4881536">10.1063/1.4881536</a>. R. Seiringer, Journal of Mathematical Physics 55 (2014). 18212018-12-11T11:54:11Z2025-09-29T13:13:35Z