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Spur

Spur[mtx1,,mtxn]
takes the trace of the product of Dirac matrices mtx1,,mtxn.

Details and OptionsDetails and Options

  • Spur takes traces in dimensions.
  • Each slot in Spur may be a linear combination of objects in spinor space (excluding Projector[][], which must occupy its own slot).
  • The following are recognized by Spur as objects in spinor space:
  • Dirac1 orunit matrix in spinor space
    DiracG or γDirac gamma matrix
    DiracG5 or γ5fifth gamma matrix
    DiracPL/DiracPR or L/Rleft/right chiral projectors
    DiracS or σgamma matrix commutator
    DiracMatrix[]sequence of multiplied objects in spinor space
    Projector[][]form factor projection operator
  • If Contract wraps Spur, tensors outside Spur are contracted into tensors appearing inside before Spur evaluates.
  • DiracG5 (γ5) anticommutes with all other gamma matrices.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

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The Feynman slash (contraction of a four-vector with the Dirac matrices) must be typed out in full:

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Constants or tensors not in spinor space appearing in Spur must be accompanied by a multiplying unit matrix ().

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The gamma-5 matrix (The '5' in γ5 should not be set in subscript):

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With left-handed projectors L:

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The gamma matrix commutator σ:

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