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DiracMatrix

Guides

  • DiracMatrix

Symbols

  • CliffordBasis
  • CliffordCanonicalBasis
  • EuclideanGammaMatrices
  • FlatMetric
  • GammaMatrices
  • MetricVielbein
  • NumericZeroQ
  • RandomCurvedMetric
  • ToDiracBasis
  • ToWeylBasis
WolframQuantumComputation`DiracMatrix`
MetricVielbein
​
MetricVielbein[η]
returns
{signature,e}
for the real symmetric metric
η
, where signature is
diag(Sign(eigenvalues))
and the vielbein
e
satisfies
T

·signature·e=η
.
​
Details and Options
​
Examples  
(6)
Basic Examples  
(1)
The vielbein of FlatMetric returns the signature itself and an identity vielbein (up to ordering and signs):
In[1]:=
MetricVielbein

FlatMetric
[1,3]
Out[1]=
{{{-1,0,0,0},{0,-1,0,0},{0,0,-1,0},{0,0,0,1}},{{0,0,0,1},{0,0,1,0},{0,1,0,0},{1,0,0,0}}}
Round-trip: reconstructing
η
from the vielbein returns the original metric (House rule #3):
In[2]:=
Moduleη=
FlatMetric
[1,3],sig,e,​​{sig,e}=
MetricVielbein
[η];​​Transpose[e].sig.e===η
Out[2]=
True
Scope  
(2)

Applications  
(1)

Possible Issues  
(1)

Neat Examples  
(1)

SeeAlso
FlatMetric
 
▪
RandomCurvedMetric
 
▪
GammaMatrices
RelatedGuides
▪
DiracMatrix
""

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