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Eps

Eps or ϵ
is the small parameter of dimensional regularization .

Details and OptionsDetails and Options

  • Eps is generated by LoopRefine to represent poles arising from UV or IR divergences.
  • Eps can be entered in StandardForm as ϵ using EsceEsc.
  • Eps formats as in TraditionalForm.
  • LoopIntegrate defines integrals with the combination (i e^(-gamma_(E)epsilon))/((4pi)^(d/2)) factored out of canonically normalized integrals typically found in one-loop calculations. This serves to abbreviate the poles near as follows:
  • LoopRefine output:implied expression:
    1/epsilon-gamma_(E)+ln(4pi)
    1/(epsilon^2)+1/epsilon(-gamma_(E)+ln(4pi))+(gamma_(E)^2)/2-gamma_(E)ln(4pi)+1/2ln^2(4pi)

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

An integral that is UV divergent:
    

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Out[1]=

Interpretation:

An integral that is IR divergent:
     where , :

In[1]:=
Click for copyable input
Out[1]=

Interpretation: