Reply to "Revisiting the solution of the second-class constraints of the Holst action"

TL;DR

This paper provides a response to previous critiques regarding the handling of second-class constraints in the Holst action, clarifying the authors' approach and addressing concerns raised in earlier work.

Contribution

It offers a detailed rebuttal and clarification of the authors' method for solving second-class constraints in the Holst action, advancing understanding in this area.

Findings

Clarifies the authors' approach to second-class constraints

Addresses and refutes previous critiques

Strengthens the theoretical foundation of the Holst action

Abstract

Reply to arXiv:1903.09201.

Full text

The authors of Montesinos:2019ypp completely misunderstood the results of our manuscript Cianfrani:2008zv . They claim that we “provided a certain parametrization of the solution of the second-class constraints resulting in a noncanonical symplectic structure (for which they also asserted to have found canonical variables). Nevertheless, such a symplectic structure is incorrect because it involves 21 variables and thus does not give the right count of the local degrees of freedom (d.o.f.) of general relativity.”

Indeed, we provided a parametrization of the phase space in terms of 24 variables, so providing the right number of degrees of freedom of General Relativity. These variables are:

• •

the connections $\tilde{A}^{a}_{i}$ and their conjugate momenta $\tilde{\pi}^{i}_{a}$, that reduce to Ashtekar-Barbero connections and inverse densitized triads in the time-gauge,

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the boost variables $\chi_{a}$ and their conjugate momenta $\tilde{\pi}^{a}$.

This is clear by looking at Eq.(12) of the paper, in which the action is written in terms of these variables.

Therefore, the motivation for the analysis given in Montesinos:2019ypp is inconsistent.