Skew Symmetric Bundle Maps on Space-Time
Daniel Henry Gottlieb (Purdue University)
TL;DR
This paper explores the Lie algebra of gauge transformations in space-time, deriving topological invariants and offering new mathematical insights into Lorentz transformations, electromagnetic duality, and related physical concepts.
Contribution
It introduces novel topological invariants from the Lie algebra of gauge transformations, providing fresh perspectives on fundamental space-time and electromagnetic phenomena.
Findings
Derived topological invariants from gauge Lie algebra
Provided new mathematical insights into Lorentz transformations
Connected gauge algebra to electromagnetic duality and energy tensors
Abstract
We study the "Lie Algebra" of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices , Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Noncommutative and Quantum Gravity Theories