What is the use of infinite-dimensional representation of group

[liucl78]

What is the use of infinite-dimensional representation of lie group?
Now, I know Hilbert space is infinite-dimensional, and physical states must be in Hilbert space.
However, for massive fields, the transformation group is SO(3), its unitary representation is finite.
For massless fields, the transformation group is non-compact ISO(2), but only the finite representation of ISO(2), namely SO(2) representation, has physical meanings.

I want to know where the infinite-dimensional representation is used in physics?

thanks

 

[Simon Bridge]

It provides the most general possible representation of what you are trying to do.