- 96-336 Schmitt T.
- Supergeometry and Quantum Field Theory, or: What is a Classical
(176K, LateX2E + AMSLaTeX)
Jul 16, 96
(auto. generated ps),
of related papers
Abstract. We discuss of the conceptual difficulties connected with the
anticommutativity of classical fermion fields, and we argue
that the "space" of all classical configurations of a
model with such fields should be described as an
infinite-dimensional supermanifold M.
We discuss the two main approaches to supermanifolds,
and we examine the reasons why many physicists tend to prefer
the Rogers approach although the Berezin-Kostant-Leites
approach is the more fundamental one. We develop the
infinite-dimensional variant of the latter, and we show that
the functionals on classical configurations considered in
a previous paper are nothing but superfunctions on M.
We present a programme for future mathematical work, which
applies to any classical field model with fermion fields. This
programme is (partially) implemented in successor papers.