Module lattice_qcd_rs::su3

Module for SU(3) matrices and su(3) (that is the generators of SU(3) )

The module defines the SU(3) generator we use the same matrices as on wikipedia divided by two such that Tr(T^a T^b) = \delta^{ab} /2 .

Constants

• GENERATORS
  list of SU(3) generators they are normalize such that Tr(T^a T^b) = \frac{1}{2}\delta^{ab}
• GENERATOR_1
  SU(3) generator
• GENERATOR_2
  SU(3) generator
• GENERATOR_3
  SU(3) generator
• GENERATOR_4
  SU(3) generator
• GENERATOR_5
  SU(3) generator
• GENERATOR_6
  SU(3) generator
• GENERATOR_7
  SU(3) generator
• GENERATOR_8
  SU(3) generator

Traits

• MatrixExpDeprecated
  Exponential of matrices.

Functions

• create_matrix_from_2_vector
  Create a super::CMatrix3 of the form [v1, v2, v1* x v2*] where v1* is the conjugate of v1 and x is the cross product.
• extract_su2_unorm
  Get the three unormalize sub SU(2) matrix of the given SU(3) matrix, ordered r, s, t see get_sub_block_r, get_sub_block_s and get_sub_block_t
• factorial_size_for_exp
  Return N such that 1/(N-7)! < f64::EPSILON.
• get_r
  Embed a Matrix2 inside Matrix3 leaving the last row and column be the same as identity.
• get_s
  Embed a Matrix2 inside Matrix3 leaving the second row and column be the same as identity.
• get_su2_r_unorm
  Get the unormalize SU(2) sub matrix of an SU(3) matrix corresponding to the “r” sub block see get_sub_block_r and su2::project_to_su2_unorm.
• get_su2_s_unorm
  Get the unormalize SU(2) sub matrix of an SU(3) matrix corresponding to the “s” sub block see get_sub_block_s and su2::project_to_su2_unorm.
• get_su2_t_unorm
  Get the unormalize SU(2) sub matrix of an SU(3) matrix corresponding to the “t” sub block see get_sub_block_t and su2::project_to_su2_unorm.
• get_sub_block_r
  get the CMatrix2 sub block corresponding to get_r
• get_sub_block_s
  get the CMatrix2 sub block corresponding to get_s
• get_sub_block_t
  Get the CMatrix2 sub block corresponding to get_t
• get_t
  Embed a Matrix2 inside Matrix3 leaving the first row and column be the same as identity.
• is_matrix_su3
  Return wether the input matrix is SU(3) up to epsilon.
• is_matrix_su3_lie
  Returns wether the given matrix is in the lie algebra su(3) that generates SU(3) up to epsilon.
• matrix_su3_exp_i
  the input must be a su(3) matrix (generator of SU(3)), gives the SU3 matrix from the adjoint rep, i.e compute exp(i v^a T^a )
• matrix_su3_exp_r
  the input must be a su(3) matrix (generator of SU(3)), gives the value exp(v^a T^a )
• orthonormalize_matrix
  Try orthonormalize the given matrix.
• orthonormalize_matrix_mut
  Orthonormalize the given matrix by mutating its content.
• random_su3
  Generate Uniformly distributed SU(3) matrix.
• random_su3_close_to_unity
  Get a radom SU(3) matrix close to [get_r] (+/- 1) * [get_s] (+/- 1) * [get_t] (+/- 1).
• reverse
  Return the matrix
• su3_exp_i
  give the SU3 matrix from the adjoint rep, i.e compute exp(i v^a T^a )
• su3_exp_r
  gives the value exp(v^a T^a )