Dear colleagues(adsbygoogle = window.adsbygoogle || []).push({});

I have recently come across a mathematical reference discussing all possible generalizations of complex numbers. A particularly interesting such generalization is known as split-complex numbers. These are defined:

z = x+jy

z* = x-jy

similarly to ordinary complex numbers except that j^2 = +1 not -1. This makes:

zz* = x^2 - y^2

Having learned about this for the first time, it immediately brought memories of a solution in supergravity that I have found but abandoned on physical grounds some time ago. It seems to me now that the solution I have found would be well-behaved, at least mathematically, if I had assumed it to be split-complex! But this begs the question: What does that mean physically? Do any of you know of any precedent in the literature.

I am just curious, but perhaps I will take a second look at that solution ...

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# Hyper-complex fields in Supergravity?

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