A Symmetry in terms of Lagrangian

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The discussion focuses on checking the invariance of terms in the Standard Model (SM) Lagrangian under the symmetries SU(3) x SU(2) x U(1). To verify gauge invariance, it is essential to ensure that each term in the Lagrangian is in the trivial representation of the SM gauge groups. If a term is in the trivial representation, it is considered gauge invariant; otherwise, it is not. This method provides a systematic approach to confirming the symmetry properties of the Lagrangian. Understanding these concepts is crucial for analyzing the underlying symmetries of the Standard Model.
zaman786
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how can we check symmetry of SM in terms of Lagrangian
Hi, as we know SM is symmetric under SU(3) X SU(2) X U(1) , But my question is , how can we check the invariance of terms in Lagrangian under these symmetries - thanks
 
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zaman786 said:
TL;DR Summary: how can we check symmetry of SM in terms of Lagrangian

Hi, as we know SM is symmetric under SU(3) X SU(2) X U(1) , But my question is , how can we check the invariance of terms in Lagrangian under these symmetries - thanks
You have to ensure that any of the terms entering the Lagrangian is in the trivial representation of the SM gauge groups. If they are, then the term is gauge invariant. If not it is not.
 
Orodruin said:
You have to ensure that any of the terms entering the Lagrangian is in the trivial representation of the SM gauge groups. If they are, then the term is gauge invariant. If not it is not.
ok- got it - thanks
 

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