A Relativity formulated in complex analysis

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1. Dec 10, 2016

vinven7

Is there a formulation of any of the relativity theories in terms of complex analysis? As in - I imagine - every event would be a complex number in a complex field.. or something as such..

2. Dec 10, 2016

robphy

3. Dec 10, 2016

Jonathan Scott

For Special Relativity, you can use a Clifford Algebra which allows you to perform Lorentz transformations (including rotations) essentially by dividing by one frame of reference and multiplying by another, and handle electromagnetism equally simply, especially Maxwell's equations and even the Dirac equation. I usually call it "Complex Four-Vector Algebra" which is a bit loose but easily understood. It is now normally known as the Algebra of Physical Space (see Wikipedia entry), and it is equivalent to the Pauli Algebra. David Hestenes previously came up with Spacetime Algebra based on the Dirac matrices which was used in a similar way, but although this makes the Dirac equation simpler it is more complicated than necessary for most other things.