====== Vacuum Expectation Value ======

<tabbox Why is it interesting?> 

Vacuum expectation values are important to describe the [[advanced_notions:symmetry_breaking:higgs_mechanism|Higgs mechanism]] and [[advanced_notions:symmetry_breaking|symmetry breaking]] in general. 

In classical field theory, we are interested in the solutions of the Yang-Mills equations and these correspond to critical points of the [[formalisms:lagrangian_formalism|action]]. 

In contrast, in quantum field theory, we use the action to compute "vacuum expectation values" of observables. A vacuum expectation value is the average measured value in the vacuum state. The thing is that many physically interesting quantities can be expressed as vacuum expectation values through various tricks.



<tabbox Layman> 

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
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<tabbox Student> 

<note tip>
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
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<tabbox Researcher> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

  
<tabbox Examples> 

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<tabbox FAQ> 
  
<tabbox History> 

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