The Trace command represents the generalized "Trace" of an object. Here the * product operator refers to the * operator of the Physics package, used to construct products involving commutative, anticommutative, or noncommutative expressions.

The %Trace command is the inert form of Trace; that is, it represents the same mathematical operation, while displaying the operation unevaluated. To evaluate the operation, use the value command.

The result returned by Trace is built as follows:

If  is a constant, then return .

If  is a single matrix, then return the trace of .

If  is a (noncommutative) product, then

If the operands are Dirac matrices or Pauli matrices, then use standard related formulas (see below).

If all of the operands are anticommutative, then

If the number of operands is even, then return 0.

Otherwise, return the Trace after normalizing the product.

If there are constants in the operands, then return the constants times the Trace of the rest.

If  is a (commutative) product, then return the constants times the Trace of the rest.

If  is a sum, not just of noncommutative objects, distribute Trace according to:.

For all other cases, return the unevaluated expression, .

The Trace of a product of Dirac matrices is based on their anticommutation relation , where g_ is the metric, and the formula is valid in 2, 3, and 4 dimensions. Thus, traces of products of an odd number of Dirac matrices are always equal to zero, while traces  of an even number (  ) of them can be expressed as a sum of terms of the form , , with the sign of each term being determined by whether the permutation of indices, from  to , is odd or even.