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group_theory:groups:infinite_dimensional_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)