TITLE: Use of traces in physics
QUESTION [9 upvotes]: This is borderline physics, but I'll post here first as it relates to a mathematical concept.
I was wondering if anyone could clarify what the physical significance is of traces, whether of matrices or more general operators, and are there more general notions of the same kind?
For example, there is what seems (as far as I can follow it) quite a promising "precursor" quantum theory called Trace Dynamics, developed by Stephen Adler and summarized in http://www.worldscinet.com/ijmpd/19/1914/free-access/S0218271810018335.pdf
Also, I have seen traces used in many other physics contexts.
I guess the first thing, more on topic here, would be to explain what mathematical significance this apparently slightly artificial (and coordinate dependent?) notion has.
Feel free to waffle in generalities - The reply needn't be impeccably formal, as I am more interested in gaining intuition than results that could easily be looked up ;-)

REPLY [4 votes]: There was a similar question recently posed (and often answered) here:
Geometric Interpretation of Trace