Pair

Description

Pair[x, y] is the head of a special pairing used in the internal representation: x and y may have heads LorentzIndex or Momentum. If both x and y have head LorentzIndex, the metric tensor is understood. If x and y have head Momentum, a scalar product is meant. If one of x and y has head LorentzIndex and the other Momentum, a Lorentz vector (p^μ) is understood.

See also:  FourVector, FV, FVD, MetricTensor, MT, MTD, ScalarProduct, SP, SPD.

Examples

This represents a four-dimensional metric tensor.

Pair[LorentzIndex[α], LorentzIndex[β]]

This is a D-dimensional metric tensor.

Pair[LorentzIndex[α, D], LorentzIndex[β, D]]

Pair[LorentzIndex[α], Momentum[p]]

Pair[Momentum[q], Momentum[p]]

Pair[Momentum[p], Momentum[p]]

Pair[Momentum[p - q], Momentum[p]]

Pair[Momentum[p], Momentum[p]]^2

Pair[Momentum[p], Momentum[p]]^3

Pair[LorentzIndex[α, n - 4], LorentzIndex[β]] // 
      Contract

ExpandScalarProduct[Pair[Momentum[p - q], Momentum[p]]]

Pair[Momentum[-q], Momentum[p]]  +  
      Pair[Momentum[q], Momentum[p]]