- #1
Professor_E
- 12
- 0
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 ...
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 ...