dd

◼ dd[expr] denotes the double dots surrounding an expression, i.e. a normal ordered string.

◼ dd is merely a placeholder. To explicitly evaluate the normal ordered expression, use normalorder.

◼ Double dotted results are returned by wick.

◼ By definition, vev[dd[expr]]=0.

◼ If pretty printing is enabled, dd is typeset as a pair of double green dots enclosing the expression.

◼ See also: normalorder, normalorderwick, wick.

Further examples

Load sneg and declare c to be a fermionic operator

<< sneg`sneg`;
snegfermionoperators[c];
ordering[c] = SEA;
snegfreeindexes[k, k1, k2, k3, 
        k4, σ1, σ2, σ3, σ4];

Evaluate vacuum expectation value either directly using vev, or by dropping the dd terms in the expression obtained by Wick's theorem.

op = nc[c[CR, k], c[AN, k]]
vev[op]
wick[op]
vev[%]

op = nc[c[CR, k1], c[AN, k2]]
vev[op]
wick[op]
vev[%]

For longer strings of operators, Wick's theorem is the only way of computing the vacuum expectation values. This can be accomplished in a single step using vevwick.

op = 
      nc[c[CR, k1, UP], c[AN, k2, UP], c[CR, k3, DO], 
        c[AN, k4, DO]]
vev[op]
wick[op]
vev[%]
% == vevwick[op]

op = 
      nc[c[CR, k1, σ1], c[AN, k2, σ2], c[CR, k3, σ3], 
        c[AN, k4, σ4]]
vev[op]
wick[op]
vev[%]
% == vevwick[op]