Details
| Original language | English |
|---|---|
| Article number | 032206 |
| Journal | Physical Review A |
| Volume | 109 |
| Issue number | 3 |
| Publication status | Published - 11 Mar 2024 |
Abstract
The Thomas-Wigner rotation (TWR) results from the fact that a combination of boosts leads to a nontrivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the nontrivially curved relativistic momentum space, i.e., the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-1/2 particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold. Interpreting TWR as a holonomy means it belongs to the same family of phenomena as Berry's phase.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A, Vol. 109, No. 3, 032206, 11.03.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Thomas-Wigner rotation as a holonomy for spin- 1/2 particles
AU - Palge, Veiko
AU - Pfeifer, Christian
N1 - Publisher Copyright: © 2024 American Physical Society.
PY - 2024/3/11
Y1 - 2024/3/11
N2 - The Thomas-Wigner rotation (TWR) results from the fact that a combination of boosts leads to a nontrivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the nontrivially curved relativistic momentum space, i.e., the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-1/2 particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold. Interpreting TWR as a holonomy means it belongs to the same family of phenomena as Berry's phase.
AB - The Thomas-Wigner rotation (TWR) results from the fact that a combination of boosts leads to a nontrivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the nontrivially curved relativistic momentum space, i.e., the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-1/2 particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold. Interpreting TWR as a holonomy means it belongs to the same family of phenomena as Berry's phase.
UR - http://www.scopus.com/inward/record.url?scp=85187540446&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.109.032206
DO - 10.1103/PhysRevA.109.032206
M3 - Article
AN - SCOPUS:85187540446
VL - 109
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 3
M1 - 032206
ER -