1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hyper-complex fields in Supergravity?

  1. Jan 11, 2009 #1
    Dear colleagues
    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 ...
  2. jcsd
  3. Jan 11, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Jan 11, 2009 #3
    Thanks - Yes I am aware to their application to special relativity. But what I am looking for is a precedent for a classical field Lagrangian that has split-complex solutions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Hyper-complex fields in Supergravity?
  1. Maximal supergravity (Replies: 4)