From: baez@rosencrantz.stcloudstate.edu ()
Subject: Re: Asymptotics of 6j symbols
Date: 11 Sep 2000 23:22:59 GMT
Newsgroups: sci.physics.research
Summary: [missing]

In article <8pfoa0$2fm$1@nnrp1.deja.com>,  <squark@my-deja.com> wrote:

>What is the original Regge calculus about?

Take spacetime and chop it into 4-simplices - which are like
tetrahedra, only 4-dimensional.  Instead of using a metric tensor,
describe the geometry of spacetime by assigning lengths to the edges
of these 4-simplices.  Then take the action for general relativity and
figure out an analogous expression that you can compute starting from
the edge-lengths of these 4-simplices.

That's the Regge calculus in a nutshell.  

For more details go back and reread "week120":

.....................................................................

In 1961 Regge came up with a discrete analog of the usual formula for
the action in classical general relativity.  It works best in
signature ++++.  His formula applies to a triangulated 4-manifold
whose edges have specified lengths.  In this situation, each triangle
has an "angle deficit" associated to it.  It's easier to visualize
this two dimensions down, where each vertex in a triangulated
2-manifold has an angle deficit given by adding up angles for all the
triangles having it as a corner, and then subtracting 2 pi.  No angle
deficit means no curvature: the triangles sit flat in a plane.  The
idea works similarly in 4 dimensions.  Here's Regge's formula for the
action: take each triangle in your triangulated 4-manifold, take its
area, multiply it by its angle deficit, and then sum over all the
triangles.

Simple, huh?  In the continuum limit, Regge's action approaches the
integral of the Ricci scalar curvature --- the usual action in general
relativity.  For more see:

T. Regge, General relativity without coordinates, Nuovo Cimento 19
(1961), 558-571.