Finite and infinite unitary transformations are determined by the nature of the symmetry group involved. Specifically, non-compact groups, such as the Lorentz group, lack finite-dimensional unitary representations, necessitating the use of infinite unitary transformations. Understanding this distinction is crucial for applications in quantum mechanics and representation theory. The discussion emphasizes that the requirement for finite or infinite transformations is dictated by the underlying mathematical structure rather than a subjective need.
PREREQUISITESPhysicists, mathematicians, and students studying quantum mechanics and representation theory, particularly those interested in the implications of symmetry groups in theoretical frameworks.
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.wasi-uz-zaman said: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