Finite and infinite unitary transformation

[wasi-uz-zaman]

hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ?
please help me in this regard.
thanks

 

[samalkhaiat]

hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ?
please help me in this regard.
thanks

It is not that "we need" or don't need, rather it is the nature of the symmetry group that decides for us. For example, non-compact groups such as the Lorentz group does not have finite-dimensional unitary representations.