A Why is 4-Momentum Conserved in Quantum Field Theory?

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In Quantum Field Theory (QFT), 4-momentum conservation arises from the symmetries of spacetime, specifically through Noether's theorem, which links symmetries to conservation laws. The Hamiltonian formalism provides a framework to derive this conservation, emphasizing that the invariance of the system under time translations leads to energy conservation, while spatial translations lead to momentum conservation. The discussion also touches on the relationship between the golden rule and conservation principles, although the primary focus remains on fundamental symmetries. In classical physics, 4-momentum conservation is similarly derived from these symmetries, reinforcing the connection between classical and quantum frameworks. Understanding these principles is crucial for comprehending the underlying mechanics of both QFT and classical physics.
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why in QFT 4-momentum is conserved?
why in QFT 4-momentum is conserved? how can it be derived from basic principles of the Hamiltonian formalism? Is it conserved because of the golden rule?
 
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Do you know why is 4-momentum conserved in classical physics? Have you heard of the Noether theorem?
 

Thread 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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