Symplectic Group Sp(K)

For a symplectic Hilbert space $(K,B)$, the symplectic group is

Key properties (paper use):

• Acts by *-automorphisms on Weyl operators: $V(z)\mapsto V(Tz)$.
• Only a subgroup is unitarily implementable in Fock space (rSp(K) ).

Example: $Sp(\mathbb R^{2n})$ is the classical real symplectic group.