- #1
liucl78
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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
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