dirac¶

This submodule implements the basic properties of 4x4 Dirac gamma matrices including their transformations under the usual discrete spacetime symmetries.

axisGamma¶

Specifies the indices from Dirac to be used for the different directions mu=0,1,2,3.

Type:: tuple[Dirac]

enum Dirac(*values)¶

Bases: CustomIndex

Valid values are as follows:

id_ = <Dirac.id_: 1>¶

g5 = <Dirac.g5: 2>¶

gw = <Dirac.gw: 3>¶

gx = <Dirac.gx: 4>¶

gy = <Dirac.gy: 5>¶

gz = <Dirac.gz: 6>¶

gw5 = <Dirac.gw5: 7>¶

gx5 = <Dirac.gx5: 8>¶

gy5 = <Dirac.gy5: 9>¶

gz5 = <Dirac.gz5: 10>¶

gwx = <Dirac.gwx: 11>¶

gwy = <Dirac.gwy: 12>¶

gwz = <Dirac.gwz: 13>¶

gxy = <Dirac.gxy: 14>¶

gxz = <Dirac.gxz: 15>¶

gyz = <Dirac.gyz: 16>¶

class Gamma(gamma: Dirac, factor: int | Fraction | Complex = 1)¶

Bases: Multiplicative

Implementation of 4d Dirac gamma matrices.

Parameters:

gamma (Dirac) – Identifier of the chosen gamma matrix.
factor (int|Fraction|Complex, optional) – Overall factor, detaults to 1.

charge()¶

Implements conventional charge conjugation.

Returns:: A copy of itself transformed accordingly.
Return type:: Block

chiralSpurion()¶

Implements conventional spurionic chiral transformation.

Returns:: Anything other than masses or Dirac gamma matrices transforms trivially under chiral spurion.
Return type:: int

reflection(mu: int)¶

Implements conventional Euclidean reflection in direction mu.

Parameters:: mu (int) – Spacetime direction.
Returns:: A copy of itself transformed accordingly.
Return type:: Block

rotation(plane: int)¶

Implements conventional 90 degree rotations in the chosen plane as defined in rotPlanes.

Parameters:: plane (int) – Identifier of the current rotational plane [0,len(rotPlanes)[.
Returns:: A copy of itself transformed accordingly.
Return type:: Block

classmethod variants()¶

Yields a generator over all declared (generalised) indices thus amounting to all the allowed index combinations.

=> May be adapted for non-trivial cases!

Returns:: Iterator over all possible variants of the particular implementation of Block.
Return type:: Iterator[Block]