- #1

liucl78

- 3

- 0

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