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PreprintCC BY 4.0arXiv

Spectroscopic structure of Non-Hermitian 𝒫𝒯-Symmetric Klein--Gordon Fields in a Magnetized Cosmic String Spacetime

  • Omar Mustafa
  • Abdullah Guvendi
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Abstract

We investigate non-Hermitian 𝒫𝒯-symmetric Klein--Gordon (KG) fields in a magnetized cosmic string spacetime. A complex non-minimal scalar interaction, β„±ΞΌ=(0,β„±r,0,0) with β„±r=Ο‰r+ibβˆˆβ„‚, indulged with a magnetic charge q=ie, is shown to introduce an effective 𝒫𝒯-symmetric Klein--Gordon oscillator supplemented by complex Coulombic and linear interactions. The resulting radial equation is shown to be conditionally exactly solvable using a biconfluent Heun series-to-polynomial approach. To observe non-Hermitian 𝒫𝒯 symmetrization, we compare with the Hermitian counterpart by mapping e=βˆ’ieΜƒ β‡’ q∈ ℝ and b=βˆ’ibΜƒ β‡’ β„±r∈ ℝ. In the limiting case Ο‰=0, the system is shown to reduce to an exactly solvable non-Hermitian 𝒫𝒯 symmetric Coulomb-type KG equation using confluent hypergeometric series/polynomials. Hereby, for both 𝒫𝒯 symmetric models considered, we show that non-Hermitian 𝒫𝒯 symmetrization introduces an upper limit for the allowed energies, unlike the corresponding Hermitian cases. These results provide an analytically tractable framework for exploring non-Hermitian relativistic quantum fields in curved spacetimes and demonstrate the role of 𝒫𝒯-symmetry in regulating the allowed spectrum.

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Cite

BibTeXRIS
BibTeX
@misc{mustafa2026spectroscopic,
  title = {{Spectroscopic structure of Non-Hermitian $\mathcalPT$-Symmetric Klein--Gordon Fields in a Magnetized Cosmic String Spacetime}},
  author = {Omar Mustafa and Abdullah Guvendi},
  howpublished = {arXiv},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2607.08148},
  eprint = {2607.08148},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.08148},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spectroscopic structure of Non-Hermitian 𝒫𝒯-Symmetric Klein--Gordon Fields in a Magnetized Cosmic String Spacetime
AU  - Omar Mustafa
AU  - Abdullah Guvendi
PY  - 2026
DA  - 2026/07/09
PB  - arXiv
DO  - 10.48550/arxiv.2607.08148
UR  - https://arxiv.org/abs/2607.08148
AB  - We investigate non-Hermitian 𝒫𝒯-symmetric Klein--Gordon (KG) fields in a magnetized cosmic string spacetime. A complex non-minimal scalar interaction, β„±_ΞΌ=(0,β„±_r,0,0) with β„±_r=Ο‰r+ibβˆˆβ„‚, indulged with a magnetic charge q=ie, is shown to introduce an effective 𝒫𝒯-symmetric Klein--Gordon oscillator supplemented by complex Coulombic and linear interactions. The resulting radial equation is shown to be conditionally exactly solvable using a biconfluent Heun series-to-polynomial approach. To observe non-Hermitian 𝒫𝒯 symmetrization, we compare with the Hermitian counterpart by mapping e=βˆ’ieΜƒ β‡’ q∈ ℝ and b=βˆ’ibΜƒ β‡’ β„±_r∈ ℝ. In the limiting case Ο‰=0, the system is shown to reduce to an exactly solvable non-Hermitian 𝒫𝒯 symmetric Coulomb-type KG equation using confluent hypergeometric series/polynomials. Hereby, for both 𝒫𝒯 symmetric models considered, we show that non-Hermitian 𝒫𝒯 symmetrization introduces an upper limit for the allowed energies, unlike the corresponding Hermitian cases. These results provide an analytically tractable framework for exploring non-Hermitian relativistic quantum fields in curved spacetimes and demonstrate the role of 𝒫𝒯-symmetry in regulating the allowed spectrum.
ER  -