TABLE OF CONTENTS
- 1. /minkowski
- 1.1. minkowski/gamma
- 1.2. minkowski/metricTensor
- 1.3. minkowski/contract
- 1.4. minkowski/abs4
- 1.5. minkowski/op_ang
- 1.6. minkowski/abs3
- 1.7. minkowski/abs4Sq
- 1.8. minkowski/SP
- 1.9. minkowski/sigma4
- 1.10. minkowski/slashed
- 1.11. minkowski/slashed5
- 1.12. minkowski/tilde
- 1.13. minkowski/levi_civita
/minkowski [ Modules ]
NAME
module minkowski
PURPOSE
This module defines functions which are connected to Relativity: Metric Tensor, Scalar Product, Gamma matrices, ...
NOTES
- Uses the "mostly -" metric.
minkowski/gamma [ Global module-variables ]
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NAME
complex, dimension(0:3,0:3,0:11), parameter :: gamma
PURPOSE
Represents the gamma matrices gamma0-gamma3, gamma5, gamma6-gamma11.
minkowski/metricTensor [ Global module-variables ]
[ Top ] [ minkowski ] [ Global module-variables ]
PURPOSE
The metric tensor
SOURCE
real, dimension(0:3,0:3), public, parameter :: metricTensor = reshape((/ 1., 0., 0., 0., & 0.,-1., 0., 0., & 0., 0.,-1., 0., & 0., 0., 0.,-1. /),(/4,4/))
minkowski/contract [ Subroutines ]
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NAME
real function Contract(a,b)
PURPOSE
INPUTS
- a,b : matrices a^(mu nu) b^(mu nu)
- The matrices can be real or complex (therefore we use an interface)
OUTPUT
- real
minkowski/abs4 [ Functions ]
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NAME
real function abs4(a) real function abs4(a, flagOk)
PURPOSE
INPUTS
- real,dimension(0:3) :: a
OUTPUT
minkowski/op_ang [ Functions ]
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NAME
real function op_ang(p1,p2)
PURPOSE
Computes the opening angle between the spatial components of two 4-vectors.
INPUTS
- real,dimension(0:3) :: p1,p2
OUTPUT
- opening angle in degrees [0...180]
minkowski/abs3 [ Functions ]
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NAME
function abs3(a)
PURPOSE
Absolute value of the spatial components of a 4-vector.
INPUTS
- real,dimension(0:3) :: a
OUTPUT
minkowski/abs4Sq [ Functions ]
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NAME
real function abs4Sq(a)
PURPOSE
Absolute value squared of a 4-Vector.
INPUTS
OUTPUT
minkowski/SP [ Functions ]
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NAME
function SP(a,b)
PURPOSE
Scalar Product for 4-Vectors, "mostly -" metric
INPUTS
- real,dimension(0:3) :: a,b ! four vectors
OUTPUT
minkowski/sigma4 [ Functions ]
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NAME
function sigma4(mu,nu) result(matrix)
PURPOSE
Returns sigma^(mu nu)=i/2 [gamma^mu, gamma^nu]
INPUTS
- integer :: mu, nu -- indices
OUTPUT
- complex, dimension(0:3,0:3) :: matrix
minkowski/slashed [ Functions ]
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NAME
function slashed(p) result(matrix)
PURPOSE
Evaluates gamma^mu*p_mu
INPUTS
- real, dimension(0:3) :: p
OUTPUT
- complex, dimension(0:3,0:3) :: matrix
minkowski/slashed5 [ Functions ]
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NAME
function slashed5(p) result(matrix)
PURPOSE
Evaluates gamma^mu*p_mu*gamma_5
INPUTS
- real, dimension(0:3) :: p
OUTPUT
- complex, dimension(0:3,0:3) :: matrix
minkowski/tilde [ Functions ]
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NAME
function tilde(a) result(a_tilde)
PURPOSE
Evaluates a^tilde=gamma_0 a^dagger gamma_0
INPUTS
- complex, dimension(0:3,0:3) :: a
OUTPUT
- complex, dimension(0:3,0:3) :: a_tilde
minkowski/levi_civita [ Functions ]
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NAME
integer function levi_civita (i, j, k, l)
PURPOSE
Calculates the fully antisymmetric Levi-Civita tensor \epsilon_{ijkl} in four dimensions.
INPUTS
- integer :: i, j, k, l --- tensor indices
OUTPUT
- tensor value for the given indices