SUNSimplify

Description

SUNSimplify simplifies products of SUNT (and complex conjugated) matrices. Basic renaming of dummy indices is done. If the option SUNTrace is set to False, then any SUNT-matrices are taken out of DiracTrace[...]; otherwise a color-trace is taken (by SUNTrace) before taking the SUN-objects in front of DiracTrace[...].

Options[SUNSimplify]

See also:  Trick.

Examples

t1 = SUNDelta[a, b] SUNDelta[b, c]

SUNSimplify[t1]

t2 = SUNT[a] . SUNT[a]

SUNSimplify[t2]

SUNSimplify[t2, SUNNToCACF -> False]

t3 = SUNF[a, r, s] SUNF[b, r, s]

SUNSimplify[t3]

t4 = SUNF[a, b, c]  .  SUNF[a, b, c]

SUNSimplify[t4]

t5 = SUNF[a, b, c] SUNF[d, b, c]

SUNSimplify[t5]

t6 = SUNF[a, b, c] SUND[d, b, c]

SUNSimplify[t6, Explicit -> True]

SUNSimplify[SUND[a, b, c] SUND[a, b, c], SUNNToCACF -> False] // 
      Factor2

SUNSimplify[SUND[a, b, c] SUND[e, b, c], SUNNToCACF -> False] // 
      FullSimplify

SUNSimplify[SUNF[a, b, c], Explicit -> True]

SUNSimplify[SUND[a, b, c], Explicit -> True]

SUNSimplify[SUNF[a, b, c] SUNT[c, b, a]]

a1 = 
      SUNF[a, b, e] SUNF[c, d, e] + SUNF[a, b, z] SUNF[c, d, z]

SUNSimplify[a1, Explicit -> False]

SUNSimplify[a1, Explicit -> False, 
      SUNIndexRename -> False]

a2 = DiracTrace[SUNT[a, b] . DiracMatrix[μ, ν]]

SUNSimplify[a2]

SUNSimplify[a2, SUNTrace -> False]

SUNSimplify[a2, SUNTrace -> False] // StandardForm

SUNSimplify[1 - SUNDelta[i1, i2]]

% // StandardForm

Clear[t1, t2, t3, t4, t5, t6, a1, a2]