FeynCalc manual (development version)

 

Nonrelativistic calculations

Since version 9.3 FeynCalc can also deal with manifestly noncovariant expressions, such as 3-vectors, Kronecker deltas and Pauli matrices

CV[p, i]

pi\overline{p}^i

CV[p, i] CV[q, i]
% // Contract

piqi\overline{p}^i \overline{q}^i

pq\overline{p}\cdot \overline{q}

CLC[i, j, k] CLC[i, j, l]
% // Contract

ϵˉijkϵˉijl\bar{\epsilon }^{ijk} \bar{\epsilon }^{ijl}

2δˉkl2 \bar{\delta }^{kl}

CSI[i, j, i]
% // PauliSimplify

σi.σj.σi\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^i

σj-\overline{\sigma }^j

PauliTrace[CSI[i, j, i, j]]
% // PauliSimplify

tr(σi.σj.σi.σj)\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^i.\overline{\sigma }^j\right)

6-6

The function LorentzToCartesian is used to break the manifest Lorentz covariance when doing nonrelativistic expansions

SP[p, q]
% // LorentzToCartesian

pq\overline{p}\cdot \overline{q}

p0q0pqp^0 q^0-\overline{p}\cdot \overline{q}