Nonrelativistic calculations
Since version 9.3 FeynCalc can also deal with manifestly noncovariant expressions, such as 3-vectors, Kronecker deltas and Pauli matrices
pi
CV[p, i] CV[q, i]
% // Contract
piqi
p⋅q
CLC[i, j, k] CLC[i, j, l]
% // Contract
ϵˉijkϵˉijl
2δˉkl
CSI[i, j, i]
% // PauliSimplify
σi.σj.σi
−σj
PauliTrace[CSI[i, j, i, j]]
% // PauliSimplify
tr(σi.σj.σi.σj)
−6
The function LorentzToCartesian
is used to break the manifest Lorentz covariance when doing nonrelativistic expansions
SP[p, q]
% // LorentzToCartesian
p⋅q
p0q0−p⋅q