Why we do not need the total Lagrangian?

[fxdung]

Total Lagrangian is very complex,but in concrete theory we use a part of Lagrangian.My question is:Why the results of a theory are the same when we use only some terms of the total Lagrangian?

 

[Orodruin]

Total Lagrangian is very complex,but in concrete theory we use a part of Lagrangian.

This is very vague. Can you give an example of what you mean?

 

[fxdung]

Example:total Standard Model consist of quark terms, gluon terms, lepton terms and electroweak boson terms sutable for SU(3)xSU(2)xU(1) symetry.But in electroweak theory when we want to calculate something instead use total Lagrangian we only use electroweak Lagrangian.My question is why the results of calculations are the same when we use the either Lagrangian?

 

[Orodruin]

The GWS Lagrangian is part of the SM Lagrangian and is sufficient whenever the strong interactions are not contributing at the relevant level. This is nothing else than disregarding higher order terms in a series expansion.

 

[fxdung]

I mean when both strong and weak interactions are present,but we want to calculate the contributions of weak force.Why we do not need total Lagrangian but GWS Lagrangian?

 

[Orodruin]

Please give a more specific example then.

 

[fxdung]

Example:when we calculate a correlation function in weak theory we only use GWS Lagrangian despite in Nature both strong and weak interaction exist

 

[Orodruin]

You are still avoiding giving a concrete example of a correlation function that you want to compute. Until you do we cannot get any further.

 

[A. Neumaier]

when both strong and weak interactions are present,but we want to calculate the contributions of weak force.Why we do not need total Lagrangian but GWS Lagrangian?

Because the weak Lagrangian defines the weak contribution to the (slightly different) total effect.

 

[fxdung]

Why is there a slightly difference between the considering total Lagrangian and only weak Lagrangian?

 

[A. Neumaier]

Why is there a slightly difference between the considering total Lagrangian and only weak Lagrangian?

Because the total Lagrangian of the standard model also contains terms involving the strong interaction.