Annals of Mathematical Sciences and Applications

Volume 7 (2022)

Number 2

Wigner rotation and its $SO(3)$ model: an active-frame approach

Pages: 141 – 166



Leehwa Yeh (Shing-Tung Yau Center, National Yang Ming Chiao Tung University, Hsinchu, Taiwan)


As an important issue in special relativity, Wigner rotation is notoriously difficult for beginners for two major reasons: this physical phenomenon is highly unintuitive, and the mathematics behind it can be extremely challenging. To remove the first obstacle, we introduce a clear and easy toy model under the guidance of group theory. To overcome the second, a concise mathematical method is developed by the integration of geometric algebra and the active-frame formalism.


Wigner rotation, special relativity, geometric algebra, Clifford algebra

Received 12 August 2022

Accepted 12 August 2022

Published 12 September 2022