Corrigendum | Open Access
Corrigendum to “Comparative Aspects of Spin-Dependent Interaction Potentials for Spin-1/2 and Spin-1 Matter Fields”
In the article titled “Comparative Aspects of Spin-Dependent Interaction Potentials for Spin-1/2 and Spin-1 Matter Fields” , calculations for some interparticle potentials for sources with spin-1/2 and spin-1 in the nonrelativistic (NR) regime contained inadvertent errors which should be corrected as follows. The main conclusions are unaltered.
We note further that we have included contact terms coming from Dirac delta contributions of the following Fourier transforms: which are the massive generalizations of the “massless” results from .
In what follows we list the corrections, indicated by , that must be added to some of the potentials given in . The mass of the mediator, , corresponds to either or , as the case may be. We also highlight that not all the potentials from  are affected and in this note we only indicate those which are modified (Moreover, we need to use in all potentials. In , we had the opposite sign, so one must make throughout.).
2. Correcting the Potentials
2.1. Potentials (Spin-1/2)
The and potentials from  are not affected. The other potentials receive partial corrections. For convenience, we define the function: so that the potentials in equations (), () (As mentioned in equation () in , the potential for has the same functional form as the potential for .), (), and () in  receive the respective corrections:
Equation (4) modifies the full potential by eliminating a momentum-independent monopole-monopole . A similar modification, but momentum-dependent, is induced by (6). For the other potentials, the modifications involve spin-spin interactions, mostly coupled to contact terms.
2.2. Potentials (Spin-1)
2.2.1. Vector Representation
2.2.2. Tensor Representation
In , equations () receive the respective corrections:
3. Concluding Remarks
The conclusions presented in  remain unaltered: in general, the interparticle potentials associated with NR spin-1/2 and spin-1 sources present similarities, especially, in the spin-spin sectors of the , , , and interactions. The most important modifications are due to the presence of contact terms, which do not play a role in macroscopic interactions.
- P. C. Malta, L. P. R. Ospedal, K. Veiga, and J. A. Helayël-Neto, “Comparative aspects of spin-dependent interaction potentials for spin-1/2 and spin-1 matter fields,” Advances in High Energy Physics, vol. 2016, Article ID 2531436, 13 pages, 2016.
- G. S. Adkins, “Three-dimensional Fourier transforms, integrals of spherical Bessel functions, and novel delta function identities,” https://arxiv.org/abs/1302.1830.
Copyright © 2017 P. C. Malta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.