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]

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

A chain of Dirac matrices with open Dirac indices

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

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

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

DCHN[SpinorUBar[p, m], i]

(uˉ(p,m))i\left(\bar{u}(p,m)\right)_i

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

DCHN[SpinorVBar[p, m], i]

(vˉ(p,m))i\left(\bar{v}(p,m)\right)_i

A single uu spinor with an open Dirac index

DCHN[i, SpinorU[p, m]]

(u(p,m))i(u(p,m))_i

A single vv spinor with an open Dirac index

DCHN[i, SpinorV[p, m]]

(v(p,m))i(v(p,m))_i

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

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

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

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

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

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

uu spinor contracted with a chain of Dirac matrices

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

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

vv spinor contracted with a chain of Dirac matrices

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

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