https://doi.org/10.1140/epjc/s10052-023-11742-1
Regular Article - Theoretical Physics
Spinor domain wall and test fermions on an arbitrary domain wall
1
Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan
2
Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan
3
Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic, 265a, Chui Street, 720071, Bishkek, Kyrgyzstan
4
Laboratory for Theoretical Cosmology, International Centre of Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
Received:
8
May
2023
Accepted:
20
June
2023
Published online:
29
June
2023
We consider a spinor domain wall embedded in a five-dimensional spacetime with a nondiagonal metric. The corresponding plane symmetric solutions for linear and nonlinear spinor fields with different parameters are obtained. It is shown that in the general case the metric functions and spinor fields do not possess 
symmetry with respect to the domain wall. We study the angular momentum density of the domain wall arising because of the presence of the spinor field creating the wall. The properties of test fermions located on an arbitrary domain wall are considered. The concepts of the “second spin” (arising due to the properties of the Lorentz group generators in a five-dimensional spacetime) and of the “second magnetic field” (representing the components 
of the electromagnetic field five-tensor) are introduced. We find eigenspinors of the “second spin” and show that some of them represent the Bell states. In the nonrelativistic limit we derive the Pauli equation for the test fermions on the domain wall which contains an extra term describing the interaction of a spin-1/2 particle with the “second magnetic field”; this allows the possibility of an experimental verification of the existence of extra dimensions.
© The Author(s) 2023
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