Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
DiracMatrix
The DiracMatrix paclet constructs Dirac gamma matrices that satisfy the Clifford anticommutation relation for an arbitrary real symmetric metric in any dimension. The flat case uses the Brauer–Weyl (Pauli–Kronecker) construction; non-flat metrics are reached through a vielbein decomposition . The package also provides basis transformations into the Dirac and Weyl (chiral) representations, and two implementations of the canonical graded Clifford operator basis: an explicit antisymmetrisation sum (pedagogically transparent) and an antisymmetric recursion (numerically stable, production-ready).
μ
γ
{,}=2I
μ
γ
ν
γ
μν
η
η
g=·η·e
T
Gamma matrices
— n gamma matrices satisfying the Clifford relation for an arbitrary real symmetric metric in any dimension
— flat Euclidean gamma matrices in the Brauer–Weyl (Pauli–Kronecker) representation
Metrics and vielbeins
— diagonal flat metric of signature (p, q)
— random real symmetric non-diagonal metric of given signature, with a controllable condition number
Basis transformations
— transform gamma matrices from the Brauer–Weyl basis to the Weyl (chiral) basis
Canonical Clifford operator basis
— graded Clifford operator basis built via an antisymmetric recursion – numerically stable, production-ready
— graded Clifford operator basis built via the explicit antisymmetrisation sum – pedagogically transparent but combinatorially expensive
Numerical utilities
— test whether every entry of an array is numerically zero, with a user-supplied tolerance
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