[Paper Review] Interaction of the generalized Duffin-Kemmer-Petiau equation with a non-minimal coupling under the cosmic rainbow gravity

M. Hosseinpour, H. Hassanabadi+3 more|arXiv (Cornell University)|Aug 29, 2021

Noncommutative and Quantum Gravity TheoriesPhysics and Astronomy75 references24 citations

TL;DR

This paper investigates the relativistic quantum dynamics of a spin-0 boson under a generalized Duffin-Kemmer-Petiau (DKP) oscillator in a cosmic string space-time with non-minimal coupling, within three distinct rainbow gravity scenarios. Using analytical methods, it derives energy eigenvalues and wave functions, revealing that the deficit angle modulates energy gaps, while rainbow gravity functions induce symmetry breaking or convergence behaviors in the spectrum, particularly in the exponential-function case where a critical cutoff frequency leads to unphysical eigenvalues.

ABSTRACT

In this study, we survey the generalized Duffin-Kemmer-Petiau oscillator containing a non-minimal coupling interaction in the context of rainbow gravity in the presence of cosmic topological defects in space-time. In this regard, we intend to investigate relativistic quantum dynamics of a spin-0 particle under the modification of the dispersion relation according to the Katanaev-Volovich geometric approach. Thus, based on the geometric model, we study the aforementioned bosonic system under the modified background by a few rainbow functions. In this way, by using an analytical method, we acquire energy eigenvalues and corresponding wave functions corresponding to each scenario. Regardless of rainbow gravity function selection, the energy eigenvalue can present symmetric, anti-symmetric, and symmetry breaking characteristics. Besides, one can see that the deficit angular parameter plays an important role in the solutions.

Motivation & Objective

• To study the relativistic quantum dynamics of a spin-0 boson under a DKP oscillator in a cosmic string background with non-minimal coupling.
• To examine the effects of rainbow gravity on the energy spectrum and wave functions via modified dispersion relations.
• To investigate how different rainbow function pairs (symmetric, asymmetric, exponential) alter the relativistic system's behavior, especially symmetry and convergence properties.
• To determine the role of the deficit angular parameter (α) in tuning energy gap widths and spectral characteristics.
• To provide analytical solutions for energy eigenvalues and corresponding DKP spinor wave functions under three distinct rainbow gravity models.

Proposed method

• Formulates the DKP oscillator with non-minimal coupling in a cosmic string metric using a tetrad formalism and spin connections.
• Applies three distinct rainbow function pairs to modify the dispersion relation: (1) symmetric g₀ = g₁ = 1/(1−εx), (2) asymmetric g₀=1, g₁=√(1−εx²), (3) exponential g₀=(e^{εx}−1)/(εx), g₁=1.
• Derives the radial equation for the first component of the DKP spinor using confluent hypergeometric functions.
• Imposes quantization conditions to obtain energy eigenvalue expressions in terms of quantum numbers n, m, and parameters M, ω, ε, α.
• Solves the radial equation analytically, expressing wave functions in terms of confluent hypergeometric functions with modified parameters depending on the rainbow function case.
• Evaluates probability density functions and performs numerical analysis to visualize energy eigenvalue and probability density behavior across different parameters.

Experimental results

Research questions

• RQ1 How does the inclusion of non-minimal coupling affect the energy spectrum of a DKP oscillator in a cosmic string space-time under rainbow gravity?
• RQ2 What are the qualitative and quantitative differences in the energy eigenvalue spectra when using three distinct rainbow function pairs?
• RQ3 How does the deficit angle parameter α influence the energy gap width and spectral symmetry?
• RQ4 Does the choice of rainbow function lead to symmetry breaking or convergence in the energy eigenvalue spectrum?
• RQ5 What is the behavior of the probability density function under different rainbow gravity scenarios, and how does it scale with energy and oscillator frequency?

Key findings

• For the first rainbow function pair (g₀ = g₁ = 1/(1−εx)), the energy eigenvalue function is asymmetric and does not converge, with the deficit angle α tuning the forbidden energy gap width.
• For the second pair (g₀=1, g₁=√(1−εx²)), the energy eigenvalue function is symmetric about zero energy, and eigenvalues converge to a constant value proportional to the inverse square root of ε at high oscillator frequencies.
• In the third case (g₀=(e^{εx}−1)/(εx), g₁=1), one branch of the energy eigenvalue function becomes unphysical beyond a critical cutoff frequency, indicating a potential symmetry-breaking phase transition.
• The probability density function increases more rapidly with energy E/Ep than the wave function magnitude alone, especially in the exponential rainbow function case.
• Numerical plots confirm that the energy eigenvalue functions are sensitive to α, with higher α values reducing the rate of increase in energy for fixed oscillator frequency.
• The radial wave functions are expressed in terms of confluent hypergeometric functions with modified parameters (e.g., κ′², ˜κ²), reflecting the energy-dependent metric structure of rainbow gravity.