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Duality invariance implies Poincaré invariance
Claudio Bunster1, Marc Henneaux
1Centro de Estudios Científicos, Casilla 1469, Valdivia, Chile.
Physical Review Letters
|February 7, 2013
Summary
This study explores dynamical theories for vector fields, revealing that spacetime structure emerges from duality principles. Key assumptions lead to Poincaré group symmetries, unifying space and time.
Area of Science:
- Theoretical Physics
- Mathematical Physics
- Dynamical Systems
Background:
- Investigating fundamental theories of physics requires understanding the emergence of spacetime.
- Dynamical theories describe how physical systems evolve over time.
Purpose of the Study:
- To explore all possible dynamical theories for two transverse vector fields evolving from a 3D Euclidean hyperplane.
- To determine if spacetime structure can emerge from fundamental principles like duality.
Main Methods:
- Considered dynamical theories with local spatial evolution.
- Imposed invariance under duality rotations of vector fields.
- Analyzed commutators of Hamiltonian and momentum densities.
Main Results:
- The evolution of vector fields necessitates specific commutator structures.
- These structures correspond to the Poincaré group or its zero signature contraction.
- Demonstrated that spacetime structure emerges from the principle of duality.
Conclusions:
- Duality rotations are a fundamental principle in constructing dynamical theories.
- The Poincaré group symmetries naturally arise from these principles.
- This work provides a novel perspective on the emergence of spacetime structure.
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