FeynCalc manual (development version)

DCHN

DCHN[x, i, j] is a chain of Dirac matrices x and is transformed into DiracChain[FCI[x],DiracIndex[i],DiracIndex[j]] by FeynCalcInternal.

See also

Overview, DiracChain, DCHN, DiracIndex, DiracIndexDelta, DiracChainJoin, DiracChainExpand, DiracChainFactor.

Examples

A standalone Dirac matrix with open Dirac indices

DCHN[GAD[\[Mu]], i, j]

\left(\gamma ^{\mu }\right){}_{ij}

A chain of Dirac matrices with open Dirac indices

DCHN[GAD[\[Mu]] . GAD[\[Nu]], i, j]

\left(\gamma ^{\mu }.\gamma ^{\nu }\right){}_{ij}

A single \bar{u} spinor with an open Dirac index

DCHN[SpinorUBar[p, m], i]

\left(\bar{u}(p,m)\right)_i

A single \bar{v} spinor with an open Dirac index

DCHN[SpinorVBar[p, m], i]

\left(\bar{v}(p,m)\right)_i

A single u spinor with an open Dirac index

DCHN[i, SpinorU[p, m]]

(u(p,m))_i

A single v spinor with an open Dirac index

DCHN[i, SpinorV[p, m]]

(v(p,m))_i

\bar{u} spinor contracted with a chain of Dirac matrices

DCHN[GAD[\[Mu]] . GAD[\[Nu]], SpinorUBar[p, m], j]

\left(\bar{u}(p,m).\gamma ^{\mu }.\gamma ^{\nu }\right){}_j

\bar{v} spinor contracted with a chain of Dirac matrices

DCHN[GAD[\[Mu]] . GAD[\[Nu]], SpinorVBar[p, m], j]

\left(\bar{v}(p,m).\gamma ^{\mu }.\gamma ^{\nu }\right){}_j

u spinor contracted with a chain of Dirac matrices

DCHN[GAD[\[Mu]] . GAD[\[Nu]], i, SpinorU[p, m]]

\left(\gamma ^{\mu }.\gamma ^{\nu }.u(p,m)\right){}_i

v spinor contracted with a chain of Dirac matrices

DCHN[GAD[\[Mu]] . GAD[\[Nu]], i, SpinorV[p, m]]

\left(\gamma ^{\mu }.\gamma ^{\nu }.v(p,m)\right){}_i