How is total angular momentum conserved in particle physics?

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Total angular momentum in particle physics is conserved and comprises both orbital angular momentum and spin angular momentum. An example illustrating this conservation can be found in specific particle interactions where certain transitions are forbidden due to angular momentum constraints. The discussion references resources that explain angular momentum in quantum mechanics and provide examples of conservation principles. Understanding these concepts is crucial for analyzing particle behavior and interactions. Overall, total angular momentum plays a vital role in the dynamics of particle physics.
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In particle physics we know that total angular momentum is conserved and its equal to orbital angular momentum plus spin angular momentum Can you give an example for me this total angular momentum conservation with explain specificly tell orbital angular momentum and spin angular momentum.
 
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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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