Summary: For a large class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold of classical solutions in Minkowski space can be constructed. This solution supermanifold carries a natural symplectic structure; the resulting Poisson brackets between the field strengths are the classical prototypes of the canonical (anti-) commutation relations. Moreover, we discuss symmetries and the Noether theorem in this context.
@article{701605,
title = {Symplectic solution supermanifolds in field theory},
booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1997},
pages = {[153]-162},
mrnumber = {MR1469032},
zbl = {0881.58024},
url = {http://dml.mathdoc.fr/item/701605}
}
Schmitt, T. Symplectic solution supermanifolds in field theory, dans Proceedings of the 16th Winter School "Geometry and Physics", GDML_Books, (1997), pp. [153]-162. http://gdmltest.u-ga.fr/item/701605/