Quantum Field Theory: A Tourist Guide for Mathematicians, by Folland.

While in Germany, I talked to Herr Professor Doctor Zeppenfield, and he told me that quantum field theory accounts for much of modern physics. So when I saw Folland's book at the library (near a book I was looking for), I was intrigued. Folland says "[the subtitle] is meant to free me and my readers from guilt about omitting various important but technical topics, viewing others from a point of view that physicists may find perverse, ..., and skipping the gruesome details of certain necessary but boring calculations". What can be better?

New in this edition: C-spheres

In general, a C-sphere is a surface in the boundary of hyperbolic space that is topologically a sphere and is foliated by chains (C-circles). One way to specify a C-circle is to give a path in homogeneous coordinates that provides vectors that are normal to the chains. The left picture is given by the path

The points corresponding to are . Taking them to produces the picture on the right.

Note: the notebook ComplexHyperbolic0.5 did not draw correct C-spheres, so it's no longer available. The code for the images above will be in CH0.6.

New in ComplexHyperbolic0.4nb:

• The animation of extors changing type (shown in CH0.3.nb post)
• A GenerateGroup command for iterating matrix group generators
• An example of using R-Balls to build fundamental domains.

The new notebook: ComplexHyperbolic0.4.nb.

A Riemannian approximation of the Heisenberg group is given by declaring the following frame field orthonormal in :

 (note that the has changed from the earlier versions).

There are many ways to approximate horisontal curves in by geodesics in the approximations . Here's one approximation, going from a sphere in Euclidean space to the apple sphere in Heisenberg space, by way of apple sets in the intermediate spaces: