Erratum to: Type-4 spinors: transmuting from Elko to single-helicity spinors

  • C. H. Coronado Villalobos
  • R. J. Bueno RogerioEmail author
  • E. F. M. T. São Sabbas
Open Access

1 Erratum to: Eur. Phys. J. C (2019) 79:308

The last co-Author’s name in the original manuscript is not correct. In Sect. 3 of the original article, the Lorentz boost parameter presented in Eqs. (15) and (18), which refers to \(\psi _{2\downarrow }(\varvec{p})\) and \(\psi _{3\downarrow }(\varvec{p})\), must to be replaced. The correct form is
$$\begin{aligned} \psi _{2\downarrow }(\varvec{p})=\sqrt{m}\left( \begin{array}{c} -i\mathcal {B}^{-}\varvec{(}p)\sin (\theta /2)e^{-i\phi /2}\\ i\mathcal {B}^{-}\varvec{(}p)\cos (\theta /2)e^{i\phi /2}\\ -\kappa _{2}\mathcal {B}^{+}\varvec{(}p)\sin (\theta /2)e^{-i\phi /2}\\ \kappa _{2}\mathcal {B}^{+}\varvec{(}p)\cos (\theta /2)e^{i\phi /2} \end{array}\right) . \end{aligned}$$
$$\begin{aligned} \psi _{3\downarrow }(\varvec{p})=\sqrt{m}\left( \begin{array}{c} i\kappa _{3}\mathcal {B}^{-}\varvec{(}p)\sin (\theta /2)e^{-i\phi /2}\\ -i\kappa _{3}\mathcal {B}^{-}\varvec{(}p)\cos (\theta /2)e^{i\phi /2}\\ -\mathcal {B}^{+}\varvec{(}p)\sin (\theta /2)e^{-i\phi /2}\\ \mathcal {B}^{+}\varvec{(}p)\cos (\theta /2)e^{i\phi /2} \end{array} \right) . \end{aligned}$$
After performing the above modification, Eqs. (26) and (27) in Sect. 5, now, are replaced by
$$\begin{aligned} \sum _{i=1}^{4}\psi _{i}(\varvec{p})\bar{\psi }_{i}(\varvec{p})=2\gamma _{\mu }p^{\mu }, \end{aligned}$$
where the matrix \(\gamma _{\mu }p^{\mu }\) reads
$$\begin{aligned}&\gamma _{\mu }p^{\mu }\nonumber \\&=\left( \begin{array}{cccc} 0 &{} 0 &{} E+p\cos (\theta ) &{} p\sin (\theta )e^{-i\phi } \\ 0 &{} 0 &{} p\sin (\theta )e^{i\phi } &{} E-p\cos (\theta ) \\ E-p\cos (\theta ) &{} -p\sin (\theta )e^{-i\phi } &{} 0 &{} 0 \\ -p\sin (\theta )e^{i\phi } &{} E+p\cos (\theta ) &{} 0 &{} 0 \end{array} \right) ,\!\!\nonumber \\ \end{aligned}$$
after Eq. (28) on the original article, the correct is to note that the spin sums is Lorentz invariant. The operator that appears on the right hand side in Eq. (3) does not annihilates type-4 spinors.

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Authors and Affiliations

  • C. H. Coronado Villalobos
    • 1
  • R. J. Bueno Rogerio
    • 2
    • 3
    Email author
  • E. F. M. T. São Sabbas
    • 1
  1. 1.Instituto Nacional de Pesquisas Espaciais (INPE)São José dos CamposBrazil
  2. 2.Instituto de Física e QuímicaUniversidade Federal de Itajubá - IFQ/UNIFEIItajubáBrazil
  3. 3.Departamento de Física e Química, Faculdade de Engenharia, GuaratinguetáUniversidade Estadual Paulista (UNESP)GuaratinguetáBrazil

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