Symmetry of the Relativistic Two-Body Bound State

Round 1

Reviewer 1 Report

This is an important paper on the relativistic quantum mechanics. It deals with two body problem for the relativistically covariant Hamiltonian. The authors employ here the Stueckelberg theory.The spectrum of a bound state of two relativistic particle quantum system is considered and the examples of Coulomb and oscillator like potentials are investigated in detail. It is shown that the spectrum of bound states is the same up to relativistic corrections as the spectrum for nonrelativistic Schroedinger equation.

The paper will be interesting for the readers working in relativistic quantum mechanics of many particles or in relativistic quantum statistical mecanics. I strongly recommend this paper for publication in Symmetry. 

Author Response

We thank the reviewer for his favorable coments.

Reviewer 2 Report

The authors have considered two body problem as bound state problem of wave function in reduced Minkowski spacetime described by coordinates (2.8). By using symmetries in such spacetime, the authors have studied a method of induced representations to obtain energy spectra related to relativistic two body bound states. I find this work interesting but I recommend the authors to revise following points:
I) It seems that some references of equations are incorrect. For example, "Eq.(5.11)" would be replaced with "Eq.(2.11)" in page 6, and "the measure (5.26)" would be replaced with "the measure (2.25)" in page 8. The authors may check the manuscript again and correct some references.
II) In page 10, instead of ladder representations, the authors used induced representations to satisfy regularities. Here, were induced representations developed by the present authors? If not so, the authors may add references in page 10.
III) Right hand side of Eq.(2.49) is omitted. The authors may correct this.

Author Response

We thank the reviewer for pointing out misprints in equation numbers an his question. Our response:

1)All equation numbers have been corrected (on p. 6 and p.8 and a couple of others).

2) The induced representation used here was developed by the authors, and we have added ref [1] in the text to make this clear. The basic idea was reviewed here because of its importance.

3) The right hand side of Eq. (2.49) (=0) has been added, we thank the reviewer for pointing this out.