Angular Momentum Operators from Quantized SO(3)

TL;DR

This paper explores how high-precision measurements could reveal a discrete structure in rotations, leading to modified angular momentum operators and fractional quantum spin values, challenging traditional quantum mechanics assumptions.

Contribution

It introduces a new form of angular momentum operators based on a modified rotation angle structure, suggesting fractional spin values at high energy scales.

Findings

Angular momentum matrices are derived for discrete rotation structures.

Quantum spin values are shifted to fractional multiples of Planck's constant.

Implication of modified quantum operators at high energy levels.

Abstract

In this paper, we will assume that the structure picture of the rotation angles will be changed according to the scale of measurement (minimum measurable angle) and if we have a device with very high accuracy (high resolution) then we can notice a discrete nature of the rotations. We derived the form of the angular momentum matrices and angular momentum operators in this case and we find an indication of the need to change all quantum mechanical operators at this very small scale (high energy level). As a physical consequence, we calculated the magnetic quantum number and find that it has been shifted to a fractional multiples of h and therefore the spin of quantum particles is no longer take integer or half integer values but some fractional values between them.