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SpinorsSimplify

Description

  • SpinorsSimplify simplifies products of $\gamma$-matrices and Dirac spinors using Dirac equation
  • By default SpinorsSimplify works in $D = 4$; for arbitrary $D$ one can use option SpinorsSimplify[[Dimension: D]]
  • One can directly set trace of identity matrix (e.g. for dimensional regularisation): SpinorsSimplify[[Dimension: D, TraceOfOne: 4]]
  • The notation for Dirac spinors should be specified using SpinorsSimplify[[u: u, v: v, uBar: uBar, vBar: vBar]]
  • By default SpinorsSimplify uses notation G_m for $\gamma_m$ and G5 for $\gamma_5$. SpinorsSimplify[[Gamma: G, Gamma5: G5]] specifies the notation for $\gamma_m$ and $\gamma_5$.
  • SpinorsSimplify[[Simplifications: rules]] will apply additional simplification rules to each processed expression

Examples

Simplify Dirac spinors in expression: 

defineMatrices 'G_a', 'G5', Matrix1.matrix, 'cu', Matrix1.covector

def sSimplify = SpinorsSimplify[[uBar: 'cu', Momentum: 'p_a', Mass: 'm']]
println sSimplify >> 'cu*G^a*p_a'.t

   > m*cu

println sSimplify >> 'cu*G_b*G^a*p_a'.t

   > -m*cu*G_{b}+2*cu*p_{b}

See also