On the cutoff parameter in the translation-invariant theory of the strong coupling polaron. (response to comments [arXiv:1204.4142] on the paper V. D. Lakhno, SSC, 152, (2012), 621)

TL;DR

This paper defends the original results on the strong coupling polaron by clarifying that previous criticisms were based on an incorrect approach to the cutoff parameter in the theory.

Contribution

It clarifies the proper treatment of the cutoff parameter in the translation-invariant theory of the strong coupling polaron, countering recent criticisms.

Findings

The original results remain valid when the cutoff parameter is correctly handled.

Criticisms based on the erroneous approach are invalid.

Proper treatment of the cutoff parameter is crucial for accurate polaron theory.

Abstract

The paper is a reply to the arguments adduced by the authors of Ref. [arXiv:1204.4142] against the results obtained by the author in Refs. [6,7]. It is shown that these arguments are based on the erroneous approach made in Ref. [arXiv:1204.4142] to the strong coupling limit when the cutoff parameter is introduced in the theory.