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PolVec

PolVec[P, pol]
represents polarization vector of vector boson with momentum P , polarization pol and implicit reference vector.
PolVec[P, pol, ref]
represents polarization vector of vector boson with momentum P , polarization pol and reference vector ref.
  • Transverse polarization vectors are lightlike four-vectors, so PolVec[P, ±1, ...] can be interpreted as massless spinor.
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Properties & Relations   (9)
With activated notation PolVec[P, pol], with P being LVector and pol interpretable as possible polarization, is denoted bypol(P) :
When first argument of PolVec is not LVector or second is not interpretable as possible polarization notation is not changed:
With activated notation PolVec[P, pol, q], with P being LVector, pol interpretable as possible polarization and q being massless Spinor, is denoted by pol(P, q):
When first argument of PolVec is not LVector, second is not interpretable as possible polarization or third is not massless Spinor notation is not changed:
To keep symbolic second argument of PolVec but still use special notation, a symbol can be set to be interpreted as possible polarization using DeclarePossiblePol:
PolVec[P, pol], with P being LVector and pol interpretable as possible polarization, is interpreted as LVector:
If first argument of PolVec is not LVector or second is not interpretable as possible polarization, then PolVec is not interpreted as LVector:
PolVec[P, pol, q], with P being LVector,pol interpretable as possible polarization and q being massless Spinor, is interpreted as LVector:
If first argument of PolVec is not LVector, second is not interpretable as possible polarization or third is not massless Spinor, then PolVec is not interpreted as LVector:
To keep symbolic second argument of PolVec but still make it interpretable as LVector,a symbol can be set to be interpreted as possible polarization using DeclarePossiblePol:
PolVec[P, ±1], with P being LVector, is interpreted as massless Spinor:
If first argument of PolVec is not LVector or second is not interpretable as ±1, then PolVec is not interpreted as massless Spinor:
PolVec[P, ±1, q], with P being LVector and q being massless Spinor, is interpreted as massless Spinor:
If first argument of PolVec is not LVector, second is not interpretable as ±1 or third is not massless Spinor, then PolVec is not interpreted as massless Spinor:
To keep symbolic second argument of PolVec but still make it interpretable as massless Spinor, a symbol can be set to be interpreted as +1 or -1 using DeclarePlusMinusOne:
Notation   (3)
With activated notation PolVec[P, pol], with P being LVector and pol interpretable as possible polarization, is denoted bypol(P) :
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When first argument of PolVec is not LVector or second is not interpretable as possible polarization notation is not changed:
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With activated notation PolVec[P, pol, q], with P being LVector, pol interpretable as possible polarization and q being massless Spinor, is denoted by pol(P, q):
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When first argument of PolVec is not LVector, second is not interpretable as possible polarization or third is not massless Spinor notation is not changed:
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To keep symbolic second argument of PolVec but still use special notation, a symbol can be set to be interpreted as possible polarization using DeclarePossiblePol:
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LVector interpretation   (3)
PolVec[P, pol], with P being LVector and pol interpretable as possible polarization, is interpreted as LVector:
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If first argument of PolVec is not LVector or second is not interpretable as possible polarization, then PolVec is not interpreted as LVector:
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PolVec[P, pol, q], with P being LVector,pol interpretable as possible polarization and q being massless Spinor, is interpreted as LVector:
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If first argument of PolVec is not LVector, second is not interpretable as possible polarization or third is not massless Spinor, then PolVec is not interpreted as LVector:
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To keep symbolic second argument of PolVec but still make it interpretable as LVector,a symbol can be set to be interpreted as possible polarization using DeclarePossiblePol:
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Spinor interpretation   (3)
PolVec[P, ±1], with P being LVector, is interpreted as massless Spinor:
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If first argument of PolVec is not LVector or second is not interpretable as ±1, then PolVec is not interpreted as massless Spinor:
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PolVec[P, ±1, q], with P being LVector and q being massless Spinor, is interpreted as massless Spinor:
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If first argument of PolVec is not LVector, second is not interpretable as ±1 or third is not massless Spinor, then PolVec is not interpreted as massless Spinor:
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To keep symbolic second argument of PolVec but still make it interpretable as massless Spinor, a symbol can be set to be interpreted as +1 or -1 using DeclarePlusMinusOne:
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Possible Issues   (1)
For massless particles longitudinal and scalar polarizations are not allowed: