Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory
Abstract
:1. Introduction
2. The CDG Decomposition—A Review
The Cho Connection
3. Rotational Gauge Symmetry in Euclidean Space
3.1. The CDG Decomposition of Gauge Theory
3.2. Monopole Field Strength
3.3. Invariant Transformations of CDG Decomposition of Gauged Rotational Theory
4. Vacuum State at One Loop
4.1. Magnitude of Monopole Condensate
4.2. Stability of the Minkowski Condensate
5. The Emergence of Effective Minkowski Space
5.1. Identifying the Local Time Axis
5.2. The Constant Speed of Light
5.3. Emergence of Lorentz Transformations
- 1.
- Linearity;
- 2.
- An internal composition law;
- 3.
- Reflection invariance.
6. Discussion
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
QCD | Quantum ChromoDynamics |
MAG | Maximal Abelian Gauge |
DOFs | Degrees of Freedom |
CDG | Cho-Duan-Ge |
Appendix A. Gauge Degrees of Freedom in SU(2)
Appendix B. General Derivation of Lorentz Transformation
- 1.
- Linearity;
- 2.
- An internal composition law;
- 3.
- Reflection invariance.
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Walker, M.L. Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory. Symmetry 2024, 16, 4. https://doi.org/10.3390/sym16010004
Walker ML. Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory. Symmetry. 2024; 16(1):4. https://doi.org/10.3390/sym16010004
Chicago/Turabian StyleWalker, Michael Luke. 2024. "Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory" Symmetry 16, no. 1: 4. https://doi.org/10.3390/sym16010004
APA StyleWalker, M. L. (2024). Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory. Symmetry, 16(1), 4. https://doi.org/10.3390/sym16010004