Why we do not need the total Lagrangian?

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Discussion Overview

The discussion revolves around the necessity of the total Lagrangian in theoretical physics, particularly in the context of the Standard Model. Participants explore why calculations using a subset of the Lagrangian, such as the electroweak Lagrangian, yield results that are consistent with those obtained using the total Lagrangian, despite the complexity of the latter.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the total Lagrangian is complex, yet calculations often rely on only a part of it, raising questions about the equivalence of results.
  • One participant provides an example from the Standard Model, indicating that the total Lagrangian includes various terms, but in electroweak theory, only the electroweak Lagrangian is used for calculations.
  • Another participant mentions that the GWS Lagrangian suffices when strong interactions are not relevant, suggesting this is akin to neglecting higher-order terms in a series expansion.
  • There is a query about why, when both strong and weak interactions are present, the GWS Lagrangian is sufficient for calculating weak force contributions.
  • Participants express the need for more specific examples, particularly regarding correlation functions in weak theory, to clarify the discussion.
  • One participant asserts that the weak Lagrangian defines the weak contribution to the total effect, implying a nuanced relationship between the two Lagrangians.
  • Questions arise about the differences between using the total Lagrangian and the weak Lagrangian, with references to the presence of strong interaction terms in the total Lagrangian.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement, particularly regarding the sufficiency of the GWS Lagrangian in certain calculations and the need for specific examples to further the discussion. No consensus is reached on the necessity of the total Lagrangian versus its subsets.

Contextual Notes

Limitations include the lack of concrete examples of correlation functions and the dependence on the definitions of terms within the Lagrangian framework. The discussion remains open-ended regarding the implications of using different Lagrangians.

fxdung
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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?
 
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fxdung said:
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?
 
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?
 
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.
 
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?
 
Please give a more specific example then.
 
Example:when we calculate a correlation function in weak theory we only use GWS Lagrangian despite in Nature both strong and weak interaction exist
 
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.
 
fxdung said:
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.
 
  • #10
Why is there a slightly difference between the considering total Lagrangian and only weak Lagrangian?
 
  • #11
fxdung said:
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.
 

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