Abstract: |
The manipulations which are used by physicists when computing with fermions (particularly classical computations) are sometimes difficult to understand from a mathematical point of view. We explain a point of view about fermion computations which was emphasized by Joseph Bernstein in lectures at the Institute for Advanced Study in 1996, and which is parallel to a familiar point of view about moduli problems in algebraic geometry. In an algebraic geometry moduli problem, it is not enough to have a space whose points are in one-to-one correspondence with isomorphism classes of algebraic varieties of a certain kind; rather, one wants a way to parameterize all algebraic families of algebraic varieties of the given kind, which leads to a functorial point of view about moduli problems. The analogous "functor of points on a supermanifold" is a way to treat routine fermion computations in a mathematically rigorous manner. |