Translation to English language of the Review written in Russian language and signed by Marachevsky V.N. on May 22, 2023 .
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Review of the supervisor for the final qualifying work
of a 2nd year Master's student of the Faculty of Physics of St. Petersburg State University
Sidelnikov Arseny Arthurovich
“Calculation of the Casimir energy and the Casimir-Polder potential for systems with sharp boundaries by methods of scattering theory”

The final qualifying work of Sidelnikov A.A. is a completed educational and scientific research carried out under my scientific supervision, relevant for modern science.

The text of the final qualifying work was written by Sidelnikov A.A. independently and has internal unity. The final qualifying work has a title page, table of contents, introduction, content, conclusion and a list of references, drawn up in accordance with the rules adopted in the scientific literature on the specialty. When completing this work, the requirements recommended in Order No. 9426/1 of 22.10.2020 for the design of the final qualifying work were met. The final qualifying work was performed using the capacities of the computing resource center of St. Petersburg State University, which is indicated in this work before the list of references in the Acknowledgements section.

The citation of literature in the final qualifying work of Sidelnikov A.A. corresponds to generally accepted ethical and legal norms. Also, there are no unauthorized borrowings in the final qualifying work of Sidelnikov A.A..

I am the supervisor of Sidelnikov A.A. in the Master's degree of the Faculty of Physics of St. Petersburg State University and was the supervisor of Sidelnikov A.A. in the Bachelor's degree of the Faculty of Physics of St. Petersburg State University. During this time, we have jointly published articles in the journals Universe and Physical Review D in open access format, and a joint article has been accepted for publication in the Russian journal PEPAN Letters. The last two works were carried out within the framework of the RSF project No. 22-13-00151. In these works, a fundamentally new gauge-invariant by construction method has been developed for calculating the Casimir forces and the Casimir-Polder potential of a neutral atom in the presence of a geometry with a flat boundary or two geometries with plane-parallel boundaries. In an article published in the journal Physical Review D, new analytical results were obtained for the Casimir-Polder potential in the presence of one or more Chern-Simons layers, including formulas for the Casimir-Polder potential in the presence of two flat Chern-Simons layers in vacuum, expressed in terms of transcendental Lerch functions and polylogarithms. Thus, this work supplemented several results of the theory of the Casimir effect expressed in terms of special functions, the result obtained is one of the fundamental results of quantum field theory. In this paper, new P-odd effects in a three-body system that occur when one of the Chern-Simons layers is rotated 180 degrees are discovered and analyzed. It is worth emphasizing that the predicted effects can be tested in a cavity using neutral atoms in the ground state described in the dipole approximation of quantum electrodynamics, while Chern insulators without an external field or systems with a quantum Hall effect in an external magnetic field can be taken as boundary layers.

Sidelnikov A.A. made an important contribution to obtaining the above-described results, the  development of a new method in the theory of the Casimir effect, while showing fluency in the apparatus of mathematical physics. The fundamental results of two published papers in the journals Universe and Physical Review D already at this point in time definitely allow to defend a dissertation for the degree of candidate of physical and mathematical sciences, I have no doubt about this due to the importance of the results obtained and the new mathematical formalism developed in these papers in the theory of the Casimir effect and the Casimir-Polder effect.

I am convinced that Sidelnikov Arseny Arthurovich is worthy of a master's degree in physics. The research work carried out by Sidelnikov A.A. deserves an excellent grade, A. I recommend Sidelnikov Arseny Arthurovich to graduate school of St. Petersburg State University, for the successful defense of his PhD thesis he actually has to successfully pass the candidate's exams in graduate school.

Scientific supervisor
Doctor of Physical and Mathematical Sciences, 
Professor of the Department of Quantum Mechanics of St. Petersburg State University
Marachevsky V.N.
May 22, 2023