Spacetime is for SU(2)
Richard Shurtleff
TL;DR
This paper explores how spacetime transformations such as rotations and boosts can be derived from the algebraic properties of the SU(2) group, linking spacetime symmetries to SU(2) representations.
Contribution
It demonstrates that spacetime generators for rotations and boosts can be constructed solely from the commutation and anticommutation relations of SU(2).
Findings
Rotations in spacetime originate from SU(2) commutation relations.
Boosts in spacetime derive from SU(2) anticommutation relations.
A unified algebraic framework for spacetime symmetries based on SU(2).
Abstract
The generators of rotations, boosts and translations are built up based on the commutation and anticommutation relations of the fundamental two dimensional representation of SU(2). Rotations in spacetime derive from the commutation relations of SU(2). Boosts derive from the anticommutation relations of SU(2).
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Taxonomy
TopicsQuantum and Classical Electrodynamics · Geophysics and Sensor Technology · Algebraic and Geometric Analysis