contraction

◼ contraction[a, b] contracts a and b.

◼ Contraction (Overscript[ab, ⎴])=ab-:ab:, where :ab: denotes normal ordered product :ab:=ab-⟨ab⟩, i.e. contraction is just the vacuum expectation value, (Overscript[ab, ⎴])=⟨ab⟩.

◼ See also: wick, normalorder, normalorderwick, vev, vevwick, contraction.

Further examples

Load sneg and declare some quantities

<< sneg`sneg`;
snegfermionoperators[c, d];
ordering[d] = SEA;
Off[General::spell];
snegfreeindexes[i, j, σi, σj];

Test the function for ordering=VACUUM

contraction[c[CR], c[AN]] == 0
contraction[c[CR], c[CR]] == 0
contraction[c[AN], c[AN]] == 0
contraction[c[CR, i], c[AN, j]] == 0
contraction[c[CR, i, σi], c[AN, j, σj]] == 
      0

contraction[c[AN], c[CR]] == 1
contraction[c[AN, i], c[CR, j]]
contraction[c[AN, i, σi], c[CR, j, σj]]

Test the function for ordering=SEA

contraction[d[CR], d[AN]]
contraction[d[CR], d[CR]] == 0
contraction[d[AN], d[AN]] == 0
contraction[d[CR, i], d[AN, j]]
contraction[d[CR, i, σi], d[AN, j, σj]]

contraction[d[AN], d[CR]]
contraction[d[AN, i], d[CR, j]] // 
      SimplifyKD
contraction[d[AN, i, σi], d[CR, j, σj]] // 
      SimplifyKD

contraction[d[CR], d[AN]]
contraction[d[CR, i], d[AN, j]] // 
      SimplifyKD
contraction[d[CR, i, σi], d[AN, j, σj]] // 
      SimplifyKD