OneLoop

Documentation unfinished ....; see also the old FeynCalc documentation at http://www.mertig.com/oldfc. NOTICE: While OneLoop is restricted to 't Hooft Feynman gauge the function OneLoopSimplify does not have this restriction (but is usually slower). OneLoop handles selfenergies, vertex and box-graphs (those only up to 3rd rank tensor in the integration variable).

WARNING: If you encounter anomalies:

\(TraditionalForm\`The\ default\ setting\ of\ $West\ is\ True, \ 
      i . e . , \ 
      the\ way\ \(tr(\(γ\^μ\) \(γ\^ν\) \(γ\^ρ\) \(γ\^σ\) \(γ\^τ\) \(γ\^λ\) γ\^5)\)\) is calculated in D dimensions has changed compared to the old FeynCalc version. Please keep in mind that the issue of (γ^5)schemes is inherintly tricky.

Description

OneLoop[q, amplitude] calculates the one-loop Feynman diagram amplitude (n-point, where n<=4 and the highest tensor rank of the integration momenta (after cancellation of scalar products) may be 3; unless OneLoopSimplify is used).

The argument q denotes the integration variable, i.e., the loop momentum. OneLoop[name, q, amplitude] has as first argument a name of the amplitude. If the second argument has head FeynAmp then OneLoop[q, FeynAmp[name, k, expr]] and OneLoop[FeynAmp[name, k, expr]] tranform to OneLoop[name, k, expr].

Options[OneLoop]

See also:  B0, C0, D0, OneLoopSimplify, TID, TIDL.

Examples

-I/Pi^2 FAD[{q, m}] // FCI

OneLoop[q, %]

mf /: MakeBoxes[mf, TraditionalForm] = 
      InterpretationBox[SubscriptBox["m", "f"], mf];

Remember that FAD[{q,mf},{q-k,mf}] is a fast possibility to enter 1/( ((q^2) - (mf^2)) ( (((q - k))^2) - 
                  (mf^2)) ).

t = 
      I ((el^2)/(16 (Pi^4) (1 - D))) FAD[{q, mf}, {q - k, mf}] 
          DiracTrace[(mf + GS[q - k]) . GA[μ] . (mf + GS[q]) . 
              GA[μ]]  //  FCI

The input to OneLoop may be in 4 dimensions, since the function changes the dimension of the objects automatically to the setting of the Dimension option (D by default).

OneLoop[q, t]

FullSimplify[%]

SP[k, r] FAD[{k, m} ,  k  -  p] // FCI

OneLoop[k, %]

Clear[t]