====== Smearing Functions ======

<tabbox Why is it interesting?> 
rfts

A typical calculation in the path integral formulation of quantum field theory requires the calculation of vacuum expectation values of products of fields. These are in general rather singular if we calculate them naively. Thus, we need to "regularize" or "smear" them, which simply means that we multiply them with a smearing function on spacetime, and then integrate, before we multiply several fields. 

In physical terms this comes about, because we never measure the value of a field at a single point, but only integrals therefore. Our real physical probes have finite size. 

For example, we must smear Wilson loops, which are then no longer lines but tori. 

(Source: Baez, Munian; Gauge Fields, Knots and Gravity, page 346)

<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.
</note>
  
<tabbox Student> 

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