Dirac oscillator in a helically twisted spacetime with axial torsion

• URL: http://arxiv.org/abs/2607.01301v2
• Date: Tue, 07 Jul 2026 12:38:54 GMT
• Title: Dirac oscillator in a helically twisted spacetime with axial torsion
• Abstract summary: We investigate the Dirac oscillator in a helically twisted spacetime endowed with a uniform axial torsion.<n>We show that the second-order problem is the ordered product $hat_+hat_-$ rather than the square of a single operator.<n>A finite-element solution reproduces the Dirac-oscillator spectrum in the flat limit.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the Dirac oscillator in a helically twisted spacetime endowed with a uniform axial torsion. Starting from an orthonormal coframe, we compute the Levi--Civita spin connection explicitly and separate the geometric contribution from the axial contortion. Retaining the matrix $β$ in the radial Moshinsky coupling, we show that the second-order problem is the ordered product $\hatΠ_+\hatΠ_-$ rather than the square of a single operator. The resulting radial dynamics is a coupled, self-adjoint two-component system in which the spin connection supplies the correct cylindrical radial operator, while the off-diagonal metric generates the helical combination $m/r-ωk$ and a Coulomb-like geometric term. A finite-element solution reproduces the planar Dirac-oscillator spectrum in the flat limit and reveals asymmetric dependence on the longitudinal momentum, avoided level crossings, and a supersymmetric zero mode at $E=Mc^2$. The axial torsion and longitudinal momentum preserve this zero mode, whereas the helical twist lifts it quadratically. Sector-resolved thermodynamic functions are obtained from the relativistic bound-state spectrum. The explicit spinors further determine longitudinal vector and axial currents, and a Witten-index analysis identifies the helical twist as the deformation that removes the protected zero mode.

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