PolarizationVector

Description

PolarizationVector[p, mu] gives a polarization vector.

See also: FourVector, Pair, Polarization.

Examples

PolarizationVector[k, μ]

Conjugate[PolarizationVector[k, μ]]

A polarization vector (Subscript[ε, μ])(k)is a special four-vector.

PolarizationVector[k, mu] // StandardForm

The transverality property (k^μ) (Subscript[ε, μ])(k)=0 is built in.

a1  =  PolarizationVector[k, μ] FourVector[k, μ]

Contract[a1]

a2  =  
      PolarizationVector[k - p, μ] FourVector[k, μ]

Contract[a2]

Depending on the alphabetical ordering of the momenta simplifcations are done, e.g., (p^μ) (Subscript[ε, μ])(k - p)=-(((k - p - k))^μ)(Subscript[ε, μ])(k - p)=(k^μ)(Subscript[ε, μ])(k - p)=k·(ε(k - p)).

a3  =  
      PolarizationVector[k - p, μ] FourVector[p, μ]

Contract[a3]

Clear[a1, a2, a3]