Remarks on the spherical waves of the Dirac field on de Sitter spacetime
Ion I. Cot\u{a}escu, Radu Racoceanu, Cosmin Crucean
TL;DR
This paper investigates solutions to the Dirac equation in de Sitter spacetime, identifying key quantum numbers and deriving a normalized solution system based on scalar momentum.
Contribution
It introduces a new normalized solution system for the Dirac equation in de Sitter spacetime, incorporating scalar momentum as a quantum number.
Findings
Eigenvalues depend on angular quantum numbers and scalar momentum
A new normalized solution system is derived
Solutions are characterized in spherical moving frames
Abstract
The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these depend on the usual angular quantum numbers and, in addition, on the value of the scalar momentum. With these elements a new result is obtained finding the system of solutions normalized (in generalized sense) in the scale of scalar momentum.
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