Matchete`
Matchete`

DiracTrace

DiracTrace[expr]

performs the Dirac trace of an expression.

Details and Options

  • The following options can be given:
  • Dimensions specifies at the assumed dimension of spacetime for the trace. Typically this will be or 4.
  • DiracTrace is a linear function and traces over Dirac spin space.
  • The trace is non-cyclic as a consequence of the dimensional continuation of γ5. See the Tech Note on Dirac Algebra for more detail on traces of γ5-odd Dirac products.

Examples

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Basic Examples  (1)

Options  (1)

Dimensions  (1)

The Dimensions option determines the dimensionality of the space in which the trace is performed. This matters when the there are repeated Lorentz indices in the Dirac product, which is contracted over the course of the trace.

Properties & Relations  (1)

DiracTrace is a linear function, e.g.,

Possible Issues  (1)

DiracTrace assumes that it is tracing over a single Dirac product. It cannot be applied to expressions with multiple Dirac products :

Note that in this example the gamma matrices are not multiplied with NonCommutativeMultiply

Tech Notes
▪
  • Dirac Algebra