TL;DR
This paper explores the relationship between spacetime transformations in an N^2-dimensional space and the algebraic structures of SU(N), linking geometric symmetries to group theoretical properties.
Contribution
It establishes a novel connection between spacetime symmetries and the algebra of SU(N), providing a new framework for understanding higher-dimensional spacetime transformations.
Findings
Rotations, boosts, and translations correspond to commutators, anticommutators, and Clebsch-Gordan coefficients of SU(N).
The work generalizes spacetime symmetry concepts to N^2 dimensions.
Provides a mathematical foundation for potential applications in theoretical physics.
Abstract
The rotations, boosts, and translations in an N^2-dimensional spacetime are shown to be related to the fundamental commutators, anticommutators, and Clebsch-Gordan coefficients, respectively, of SU(N).
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Relativity and Gravitational Theory