FeynCalc manual (development version)

Amplitude

Amplitude is a database of Feynman amplitudes. Amplitude["name"] returns the amplitude corresponding to the string "name". A list of all defined names is obtained with Amplitude[]. New amplitudes can be added to the file "Amplitude.m". It is strongly recommended to use names that reflect the process.

The option Gauge -> 1 means `t Hooft Feynman gauge;

Polarization -> 0 gives unpolarized OPE-type amplitudes, Polarization -> 1 the polarized ones.

See also

Overview, FeynAmp.

Examples

Amplitude[] // Length

9898

This is the amplitude of a gluon self-energy diagram:

Amplitude["se1g1"] 
 
Explicit[%] 
  
 

SUNDeltaContract(fFCGV(a)FCGV(c)FCGV(e)fFCGV(b)FCGV(d)FCGV(f)ΠFCGV(e)FCGV(f)FCGV(β)FCGV(σ)(FCGV(q))VFCGV(μ)FCGV(α)FCGV(β)(FCGV(p)  FCGV(q)FCGV(p)FCGV(q))VFCGV(ν)FCGV(ρ)FCGV(σ)(FCGV(p)  FCGV(p)FCGV(q)  FCGV(q))ΠFCGV(c)FCGV(d)FCGV(α)FCGV(ρ)(FCGV(p)FCGV(q)))\text{SUNDeltaContract}\left(f^{\text{FCGV}(\text{a})\text{FCGV}(\text{c})\text{FCGV}(\text{e})} f^{\text{FCGV}(\text{b})\text{FCGV}(\text{d})\text{FCGV}(\text{f})} \Pi _{\text{FCGV}(\text{e})\text{FCGV}(\text{f})}^{\text{FCGV}(\beta )\text{FCGV}(\sigma )}(\text{FCGV}(\text{q})) V^{\text{FCGV}(\mu )\text{FCGV}(\alpha )\text{FCGV}(\beta )}(\text{FCGV}(\text{p})\text{, }\;\text{FCGV}(\text{q})-\text{FCGV}(\text{p})\text{, }-\text{FCGV}(\text{q})) V^{\text{FCGV}(\nu )\text{FCGV}(\rho )\text{FCGV}(\sigma )}(-\text{FCGV}(\text{p})\text{, }\;\text{FCGV}(\text{p})-\text{FCGV}(\text{q})\text{, }\;\text{FCGV}(\text{q})) \Pi _{\text{FCGV}(\text{c})\text{FCGV}(\text{d})}^{\text{FCGV}(\alpha )\text{FCGV}(\rho )}(\text{FCGV}(\text{p})-\text{FCGV}(\text{q}))\right)

1FCGV(q)2(FCGV(p)FCGV(q))2gs2gFCGV(α)FCGV(ρ)gFCGV(β)FCGV(σ)fFCGV(a)FCGV(d)FCGV(f)fFCGV(b)FCGV(d)FCGV(f)(gFCGV(β)FCGV(μ)(FCGV(p)FCGV(α)FCGV(q)FCGV(α))+gFCGV(α)FCGV(μ)(2  FCGV(p)FCGV(β)FCGV(q)FCGV(β))+gFCGV(α)FCGV(β)(2  FCGV(q)FCGV(μ)FCGV(p)FCGV(μ)))(gFCGV(ρ)FCGV(σ)(FCGV(p)FCGV(ν)2  FCGV(q)FCGV(ν))+gFCGV(ν)FCGV(σ)(FCGV(p)FCGV(ρ)+FCGV(q)FCGV(ρ))+gFCGV(ν)FCGV(ρ)(FCGV(q)FCGV(σ)2  FCGV(p)FCGV(σ)))-\frac{1}{\text{FCGV}(\text{q})^2 (\text{FCGV}(\text{p})-\text{FCGV}(\text{q}))^2}g_s^2 g^{\text{FCGV}(\alpha )\text{FCGV}(\rho )} g^{\text{FCGV}(\beta )\text{FCGV}(\sigma )} f^{\text{FCGV}(\text{a})\text{FCGV}(\text{d})\text{FCGV}(\text{f})} f^{\text{FCGV}(\text{b})\text{FCGV}(\text{d})\text{FCGV}(\text{f})} \left(g^{\text{FCGV}(\beta )\text{FCGV}(\mu )} \left(-\text{FCGV}(\text{p})^{\text{FCGV}(\alpha )}-\text{FCGV}(\text{q})^{\text{FCGV}(\alpha )}\right)+g^{\text{FCGV}(\alpha )\text{FCGV}(\mu )} \left(2 \;\text{FCGV}(\text{p})^{\text{FCGV}(\beta )}-\text{FCGV}(\text{q})^{\text{FCGV}(\beta )}\right)+g^{\text{FCGV}(\alpha )\text{FCGV}(\beta )} \left(2 \;\text{FCGV}(\text{q})^{\text{FCGV}(\mu )}-\text{FCGV}(\text{p})^{\text{FCGV}(\mu )}\right)\right) \left(g^{\text{FCGV}(\rho )\text{FCGV}(\sigma )} \left(\text{FCGV}(\text{p})^{\text{FCGV}(\nu )}-2 \;\text{FCGV}(\text{q})^{\text{FCGV}(\nu )}\right)+g^{\text{FCGV}(\nu )\text{FCGV}(\sigma )} \left(\text{FCGV}(\text{p})^{\text{FCGV}(\rho )}+\text{FCGV}(\text{q})^{\text{FCGV}(\rho )}\right)+g^{\text{FCGV}(\nu )\text{FCGV}(\rho )} \left(\text{FCGV}(\text{q})^{\text{FCGV}(\sigma )}-2 \;\text{FCGV}(\text{p})^{\text{FCGV}(\sigma )}\right)\right)