SpAssoc

SpAssoc[P]
represents lightlike vector associated with four-vector P through light cone decomposition with default reference vector.
SpAssoc[P, ref]
represents lightlike vector associated with four-vector P through light cone decomposition with (massless or massive) reference vector ref.
  • SpAssoc[P] for P being LVector labels lightlike four-vector where qP denotes default reference vector SpRef[P].
  • SpAssoc[P, q] for P being LVector and q being massless Spinor labels lightlike four-vector .
  • SpAssoc[P, Q] for P being LVector and Q being massive LVector labels lightlike four-vector PQ obtained by "simultaneous" lightcone decomposition of P and Q such that: and .
With activated notation SpAssoc[P], with P being LVector, is denoted by P:
When argument of SpAssoc is not LVector notation is not changed:
With activated notation SpAssoc[P, Q], with P and Q being LVectors, is denoted by PQ:
When arguments of SpAssoc are not LVectors notation is not changed:
SpAssoc[P], with P being LVector, is interpreted as massless Spinor:
If argument of SpAssoc is not LVector, then SpAssoc is not treated as Spinor:
SpAssoc[P, Q], with P and Q being LVectors, is interpreted as massless Spinor:
If arguments of SpAssoc are not LVectors, then SpAssoc is not treated as Spinor:
Default numerical components for SpAssoc[P], with P being LVector with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument (this will also automatically set default numerical values for SpRef[P] if it was not set earlier):
Numerical values obtained this way are equal to following combination of numerical values of P and SpRef[P]:
Default numerical components for SpAssoc[P, q], with P being LVector and q being massless Spinor both with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
Numerical values obtained this way are equal to following combination of numerical values of P and q:
Default numerical components for SpAssoc[P, Q], with P and Q being LVectors with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
Numerical values obtained this way are equal to following combination of numerical values of P , Q and QP:
When DeclareSpinorMomentum, with SpAssoc[P, Q] as only argument, is called when P or Q does not have declared numerical components declaration fails and a warning message is printed:
With activated notation SpAssoc[P], with P being LVector, is denoted by P:
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When argument of SpAssoc is not LVector notation is not changed:
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With activated notation SpAssoc[P, Q], with P and Q being LVectors, is denoted by PQ:
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When arguments of SpAssoc are not LVectors notation is not changed:
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SpAssoc[P], with P being LVector, is interpreted as massless Spinor:
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If argument of SpAssoc is not LVector, then SpAssoc is not treated as Spinor:
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SpAssoc[P, Q], with P and Q being LVectors, is interpreted as massless Spinor:
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If arguments of SpAssoc are not LVectors, then SpAssoc is not treated as Spinor:
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Default numerical components for SpAssoc[P], with P being LVector with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument (this will also automatically set default numerical values for SpRef[P] if it was not set earlier):
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Numerical values obtained this way are equal to following combination of numerical values of P and SpRef[P]:
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Default numerical components for SpAssoc[P, q], with P being LVector and q being massless Spinor both with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
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Numerical values obtained this way are equal to following combination of numerical values of P and q:
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Default numerical components for SpAssoc[P, Q], with P and Q being LVectors with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
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Numerical values obtained this way are equal to following combination of numerical values of P , Q and QP:
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When DeclareSpinorMomentum, with SpAssoc[P, Q] as only argument, is called when P or Q does not have declared numerical components declaration fails and a warning message is printed:
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