Abstract
We give a geometrical description of the double covering of the two-dimensional de Sitter universe as a coset space of the group SL(2, R). This identification is helpful in characterizing the de Sitter covariance of Dirac fields on the two-dimensional de Sitter spacetime or its double covering and opens the possibility to study CFT on that manifolds.
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Notes
- 1.
If the function f is also anti-periodic, i.e. if \( f(t,\theta +2\pi )= -f(t,\theta )\) the matrix \(S_f\) is well defined on the de Sitter hyperboloid \({dS_2}\) itself. However in this case we cannot solve the Dirac-Fock-Ivanenko equation with zero potential.
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Moschella, U. (2018). Two Dimensional de Sitter Spinors and Their SL(2, R) Covariance. In: Antoine, JP., Bagarello, F., Gazeau, JP. (eds) Coherent States and Their Applications. Springer Proceedings in Physics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-76732-1_13
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