We describe the action of symplectic group on homogeneous space squeezed states (quantum blobs) and extend this to semigroup. then metaplectic representation (or oscillator) semigroup study properties such an extension using Bargmann-Fock space. The shape geometry squeezing is analyzed noncommuting elements from are proposed be used in simultaneous monitoring quantum variables — which should le...

We employ a simple and accurate dimensional interpolation formula for the shapes of random walks at $D=3$ $D=2$ based on analytically known solutions both limits $D=\infty$ $D=1$. The results obtained radii gyration an arbitrary shaped object are about $2\%$ error compared with numerical $D = 3$ 2$. also calculated asphericity three-dimensional walk using formula. Result agrees very well numeri...