Modifications to Quantum Theory in Curved Spacetime

Recent research by Mytraya Gattu and S. Shankaranarayanan, titled "Extended Uncertainty Principle via Dirac Quantization," explores significant modifications to quantum theory when applied to curved spacetime. This study, available on arXiv, highlights how traditional approaches have primarily focused on ultraviolet (UV) modifications, while this work emphasizes the importance of infrared (IR) modifications.

The authors demonstrate that the changes to the position-momentum algebra are directly related to curvature invariants, such as the Ricci scalar and Kretschmann scalar. This finding suggests that the effects of spacetime curvature are not just theoretical but can be derived axiomatically through Dirac's quantization procedure.

The study also investigates particle dynamics within arbitrary curved spacetimes by embedding them into a higher-dimensional flat geometry. This innovative approach allows for a more comprehensive understanding of particle behavior in four-dimensional curved spacetime, revealing that the corrections due to curvature are universal across various spacetimes.

Moreover, the implications of these findings extend to critical areas in physics, such as black hole physics and quantum entanglement. The authors compare their results with existing extended uncertainty principles, providing a broader context for their conclusions. This research contributes to the ongoing discourse on unifying quantum mechanics and general relativity, a fundamental challenge in modern physics.

For further details, the paper can be cited as follows: Gattu, M., & Shankaranarayanan, S. (2022). Extended Uncertainty Principle via Dirac Quantization. arXiv:2204.01780.