Re: Chern-Simons theory challenge

An example of exceptionally good pop science:
http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf


An attempt to start a pop science explanation of Chern-Simons theory:

Every point in space-time has a copy of a vector space, called a fiber
bundle; the fibers are the vector spaces. The vectors in these internal
spaces, spread out over real space, are the matter field. The
connection specifies how to compare vectors attached to different
points (by parallel transport). If, when you move along a closed path,
the vector you start with is different from the one you end with, then
the connection is curved. Both fields, matter and connection (also
called gauge field), vary over time, obeying a principle of least
action.

Chern-Simons theory is a topological gauge theory in three dimensions
which describes knot and three-manifold invariants. There is a
correspondence to topological string theory, which is related to
Gromov-Witten invariants.

References:
A Unified Grand Tour of Theoretical Physics, Ian Lawrie
Chern-simons Theory, Matrix Models, And Topological Strings, Marcos
Marino


An answer to Daniel:

Asset price bundles are vectors in asset space. Calculating net present
values is parallel transporting these vectors along a connection. The
connection includes prices and discounting as its spatial and temporal
elements. Curvature is excess return.

Reference:
Physics of Finance, Kirill Ilinski

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