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## Main Question or Discussion Point

I read somewhere that the irreducible representations of Lie groups were countable. But what about translations? Isn't each momentum value its own irreducible singlet, and there are a continuum of momentum values?

For example take [tex]e^{ipx} [/tex]. If you translate it, it doesn't mix with anything else, it remains the same state. There are infinite number of momentum p, therefore infinite number of irreducible represetations.

For example take [tex]e^{ipx} [/tex]. If you translate it, it doesn't mix with anything else, it remains the same state. There are infinite number of momentum p, therefore infinite number of irreducible represetations.