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arXiv · 2607.01301

Dirac oscillator in a helically twisted spacetime with axial torsion

Matheus D. Moro·Fabiano M. Andrade·Faizuddin Ahmed·Edilberto O. Silva
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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 $\beta$ in the radial Moshinsky coupling, we show that the second-order problem is the ordered product $\hat\Pi_+\hat\Pi_-$ 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 $m/r-\omega k$ 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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Matheus D. Moro, Fabiano M. Andrade, Faizuddin Ahmed, Edilberto O. Silva. 2026-07-01. Dirac oscillator in a helically twisted spacetime with axial torsion. https://arxiv.org/abs/2607.01301

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