Local Space-Time Curvature Effects on Quantum Orbital Angular Momentum

TL;DR

This paper explores how local space-time curvature influences quantum orbital angular momentum, revealing potential half-integer projections while maintaining integer quantum numbers, and linking gravitational effects to the spin-2 nature of gravity.

Contribution

It introduces an extended orbital angular momentum operator accounting for gravitational effects, showing the emergence of half-integer projections in curved space-time.

Findings

Half-integer m states appear due to curvature effects.

Half-integer m states vanish in flat space-time.

Minimum orbital quantum number l=2 is required for gravitational effects.

Abstract

This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due to gravitation can identify the existence of orbital states with half-integer projection quantum numbers "m" along the axis of quantization, while still preserving integer-valued orbital quantum numbers "l" for a simply connected topology. The consequences of this possibility are explored in depth, noting that the half-integer "m" states vanish as required when the locally curved space-time reduces to flat space-time, fully recovering all established properties of orbital angular momentum in this limit. In particular, it is shown that a minimum orbital number of "l = 2" is necessary for the gravitational interaction to appear within this context, in perfect correspondence with the spin-2 nature of linearized general relativity.