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arXiv:2012.14282 · Journal of Physics A Mathematical and Theoretical

Reply to comment on ‘The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass’

R R S Oliveira, A A Araújo Filho, R V Maluf, C A S Almeida

Published Dec 7, 2020• 4 citations
arXivHTMLPDF

Abstract

Abstract It is shown that the results of our paper are correct, although the use of the chirality operator γ 5 = σ 1 in the paper is not correct, as fairly the authors of the comment stated.
DOI
10.1088/1751-8121/abd154

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Abstract It is shown that the paper ‘The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass’ recently published in this journal has fulcrum on false assertions.

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The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.
We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.