Orthochorous? Don't think I've heard that term before

[Fredrik]

An arbitrary Lorentz transformation $\Lambda$ in 1+1 dimensions can be written as
\begin{align}
\Lambda=\frac{\sigma}{\sqrt{1-v^2}}
\begin{pmatrix}1 & -v\\ -\rho v & \rho\end{pmatrix}.
\end{align} Here $\sigma=\operatorname{sgn}\Lambda_{00}$ and $\rho=\det\Lambda$. I learned today that $\Lambda$ is said to be orthochorous if $\sigma\rho=1$. I don't think I've ever heard that term before. (I found it in Streater & Wightman...which by the way is the second hit if I google the term). Can someone explain this term? Is it standard? What does the "chorous" part refer to? Now that I think about it, I realize that I don't even know what "ortho" means, so I wouldn't mind getting that explained too.

And no, I'm not misspelling "orthochronous". This is a different word.

 

[dx]

In thermodynamics, an 'isochoric' process is one where the volume remains constant, so I'm guessing 'chorous' in orthochorous means volume. And ρ = det Λ is the factor by which the transformation changes volumes.

 

[Mordred]

Orthochorous is another subgroup where orthochronus preserves the direction of time. Orthochorus preserves the sign of the volume of space (Lorentz transformations)

http://books.google.ca/books?id=RfR...=0CEMQ6AEwBA#v=onepage&q=orthochorous&f=false

this link has some of the various subgroups and mathematics involved

edit : its kind of strange that one can find dozens of links describing the subgroups orthochronous, proper, and restricted but finding coverage of orthochorous is almost non existant.

 

[Mordred]

http://books.google.ca/books?id=YBd...q=orthochorous lorentz transformation&f=false

section 6.3 of this article covers some of the sub groups, took a bit to find it hope that helps

 

[Fredrik]

section 6.3 of this article covers some of the sub groups, took a bit to find it hope that helps

It might, but I think I understand the subgroups well enough. I'm mainly concerned with the terminology right now.

Based on what you guys said, it seems likely that some form of the word "chorous" means "volume". Thanks both of you.

 

[dextercioby]

Well, as per original ancient Greek, it doesn't

<Etymology

The noun isochor and the adjective isochoric are derived from the Greek words ἴσος (isos) meaning "equal", and χώρος (choros) meaning "space."> (from here).

Also χῶρος LSJ, Middle Liddell, Slater, Autenrieth 2.422 0 a definite space, piece of ground, place
χώρα LSJ, Middle Liddell, Slater 15.125 2 space

In addition
http://www.perseus.tufts.edu/hopper/definitionlookup?type=begin&q=volume&target=greek