group_theory:groups:infinite_dimensional_groups

While finite dimensional Lie groups and their representations are rather wellunderstood mathematical objects, this is not at all true for infinite dimensional Lie groups, where only a fragmentary such understanding is available. In earlier chapters we have studied in detail what happens when quantizing a finite dimensional phase space, bosonic or fermionic. In these cases a finite dimensional symplectic or orthogonal group acts and quantization uses a representation of these groups.

For the case of quantum field theories with their infinite dimensional phase spaces, the symplectic or orthogonal groups acting on these spaces will be infinite dimensional.https://www.math.columbia.edu/~woit/QM/qmbook.pdf

group_theory/groups/infinite_dimensional_groups.txt · Last modified: 2017/12/06 09:33 (external edit)