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Vector Form of Symmetry Degree
G H Dong1, Z W Zhang2, C P Sun1
1Beijing Computational Science Research Center, Beijing, 100084, China.
Scientific Reports
|October 13, 2017
Summary
We introduce the vector form of symmetry degree (VSD) to quantify system asymmetry. VSD offers richer information than scalar symmetry degree (SSD) for analyzing symmetry breaking in physical systems.
Area of Science:
- Physics
- Quantum Mechanics
- Group Theory
Background:
- Symmetry degree quantifies system asymmetry relative to symmetry groups.
- Scalar form of symmetry degree (SSD) provides a quantitative description.
- Existing methods lack detailed information on symmetry breaking.
Purpose of the Study:
- Introduce the vector form of symmetry degree (VSD) as an advancement over SSD.
- Demonstrate VSD's superior capabilities in analyzing symmetry and asymmetry.
- Provide a more comprehensive framework for understanding symmetry breaking phenomena.
Main Methods:
- Define VSD dimension by the conjugacy class number of the symmetry group.
- Relate VSD's squared length to SSD.
- Determine VSD direction using conjugacy class orders.
- Model VSD evolution under symmetry breaking perturbations.
Main Results:
- VSD provides additional information on broken symmetry operators.
- VSD distinguishes distinct symmetry breaking perturbations causing degenerate SSD.
- VSD evolution equation describes symmetry breaking effects.
- VSD effectively analyzes accidental degeneracy and spontaneous symmetry breaking.
Conclusions:
- VSD offers a more detailed and informative characterization of symmetry than SSD.
- VSD enhances the understanding of symmetry breaking, degeneracy, and spontaneous symmetry breaking.
- The vector form of symmetry degree is a powerful tool for physical system analysis.
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