On the Role of Constraints and Degrees of Freedom in the Hamiltonian Formalism

Round 1

Reviewer 1 Report

This is a competent paper on the constrained Hamiltonian formalism, with stimulating comments on the existing literature. I think it constitutes a valid addition to this literature. 

Author Response

Thank you for your very positive evaluation of my work.

Reviewer 2 Report

Author give a pedagogical introduction to the degenerate Hamiltonian systems,  showing both very simple mechanical examples and general
arguments about how it works.  For the familiar field theory models, He explain why the gauge freedom there "hits twice" in the sense of producing twice as many first-class constraints as gauge symmetries, and why primary, and only primary, constraints should be put into the total Hamiltonian. In this paper, has been shown how the Hamiltonian analysis works in the simplest mechanical cases, and also mentioning some modern physics issues. Author review some
applications to electromagnetism and gravity in a bit more detail.

Author Response

Thank you for your positive comments.

Reviewer 3 Report

I’m sorry but I’m not able to follow the line of reasoning of this manuscript.

Sometimes the style is more similar to a conversation than to a scientific paper (e.g. “This is totally wrong!”, “No, this is not a gauge choice!”, etc. )

The paper concerns Hamiltonian systems with constraints. The topic was originally studied by Paul Adrien Maurice Dirac in the Sixties and it is discussed in many textbooks. As far as I understand this paper does not address a specific gap in the field. The author is not in agreement with most of the literature on the argument and makes quite strong claims in strong disagreement with the mail references on this topic (e.g. “It is often stated, for example in the classic book of Henneaux and Teitelboim [5], that it is more natural  to take both primary and secondary constraints on equal footing. This is totally wrong!” (line 255)).

I do not think the manuscript provides a real improvement in the field.I can not understand the line of the manuscript in several points. E.g., in Sect. 4.1 the total Hamiltonian seems different from the Hamiltonian discussed by Dirac in his “Lectures on quantum mechanics” (1964), p 27-32, I can not see the usual term A_0 \pi_i,i

I suggest a careful reading of “Lectures on quantum mechanics” by Dirac and “Quantization of Gauge Systems” by Henneaux and Teitelboim. 

Author Response

Sorry, I don't see what is the problem with following the reasoning. For example, when I say "this is not a gauge choice", I immediately explain why.

1. Yes, indeed, what I say is different from most references on the subject. This is precisely my point. Most of the available treatments do have false statements, and I explain where and why.
 
2. My Hamiltonian in the Section 4.1 did have a typo. I thank the Referee for noticing that. Of course, its second term contains A_0, and not A_i. I corrected that.

Round 2

Reviewer 3 Report

The paper can be accepted in the present form.