Moataz
Jan15-09, 06:00 AM
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 ...
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 ...