Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quaternion complex calculus?

  1. Sep 11, 2006 #1
    "Quaternion complex calculus?"..

    Hello my question is if there exist an analogue of "complex calculus" for complex numbers but using "quaternions"..in fact if we define the Quaternion.. [tex] a+ib+jc+kd [/tex] with the "commutation relations" [tex] [x_i ,x_j ]=\epsilon _{ijk} x_k [/tex] then i would like to know if there exist the equivalent to..

    a) "Cauchy-Riemann" equation...( Harmonic functions ?)

    b) "cauchy integral formula" (for Surface, Volume or line integrals on this space)

    Of course the can be very 2fruitful" specially when studying Relativity since you could consider the Quaternion:

    [tex] Q= cdt-idx-jdy-kdz [/tex] (x,y,z) space coordinates and t the time.:grumpy: :grumpy:
  2. jcsd
  3. Sep 11, 2006 #2
    There is a nice website that maintains info and links about http://www.greenspun.com/bboard/q-and-a.tcl?topic=quaternions" [Broken].
    Last edited by a moderator: May 2, 2017
  4. Sep 11, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Much of what's interesting is simply vector analysis in disguise. It would be good to look at that.
    Last edited: Sep 11, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Quaternion complex calculus Date
Quaternion Derivative Sep 28, 2015
Covariance of small angle quaternion May 15, 2012
Quaternion derivative Jul 8, 2009
Quaternion calculus. Aug 15, 2008