Finite and infinite unitary transformation

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Finite and infinite unitary transformations are determined by the nature of the symmetry group involved. Non-compact groups, like the Lorentz group, do not possess finite-dimensional unitary representations. Understanding these transformations is crucial for applications in quantum mechanics and quantum field theory. The distinction between finite and infinite transformations is essential for analyzing different physical systems. Ultimately, the requirement for these transformations arises from the underlying mathematical structures of the theories being studied.
wasi-uz-zaman
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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
 
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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
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.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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