src/module/spinor [ Modules ]
NAME
Module spinor
USAGE
use spinor
DESCRIPTION
This module contains all the function to compute the spinorial products, scalar products and epsilon_tensor
OUTPUT
It exports:
* ket -- a function to compute the ket spinor
* bra -- a function to compute the bra spinor
* pslash -- a function to compute p^{\mu} \gamma_{\mu}
* bra_ket -- a function to compute the spinorial product
* eps_prod_sca -- a function to compute the scalar product e_i.p_j
* eps_prod_eps -- a function to compute the scalar product e_i.e_j
* scalar -- a function to compute the scalar product
* e_ -- a function to compute the epsilon tensor
USES
* precision_golem (src/module/precision_golem.f90)
src/module/spinor/bra [ Functions ]
NAME
Function bra
USAGE
complex_dim1_4 = bra(p,i)
DESCRIPTION
This function computes the spinor bra using
bra(p) = ket(p)^{\dagger} \gamma_0
modified for non physical configuration p_0 < 0.
The functions bra and ket verify the conditions:
<-p-|q+> = <p-|-q+> = i <p-|q+>
<-p+|q-> = <p+|-q-> = i <p+|q->
<-p-|-q+> = - <p-|q+>
<-p+|-q-> = - <p+|q->
INPUTS
* p -- a real array (type ki) of rank 1, shape 4; a 4-momentum * i -- an integer, the value of the helicity (= 1,-1)
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex array (type ki) of rank 2 and shape 1,4
EXAMPLE
src/module/spinor/bra_ket [ Functions ]
NAME
Function bra_ket
USAGE
complex = bra_ket(p1,i1,p2,i2,k1,k2,k3,k4,k5,k6,k7,k8,k9,k10)
DESCRIPTION
This function computes <p1 i1|k1slash*k2slash*...*k10slash|p2 i2> i1 and i2 = +/- 1 are the helicities where the inner argument k1slash,k2slash,...,k10slash are optional
INPUTS
* p1 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * i1 -- an integer, the value of the helicity (= 1,-1) * p2 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * i2 -- an integer, the value of the helicity (= 1,-1) * k1 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k2 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k3 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k4 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k5 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k6 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k7 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k8 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k9 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional * k10 -- a real array (type ki) of rank 1, shape 4; a 4-momentum optional
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex (type ki)
EXAMPLE
src/module/spinor/e_ [ Functions ]
NAME
Function e_
USAGE
complex = e_(k1,k2,k3,k4)
DESCRIPTION
This function gives the antisymetric tensor epsilon From Thomas Reiter
INPUTS
* k1 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * k2 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * k3 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * k4 -- a real array (type ki) of rank 1, shape 4; a 4-momentum
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex (type ki)
EXAMPLE
src/module/spinor/eps_prod_eps [ Functions ]
NAME
Function eps_prod_eps
USAGE
complex = eps_prod_eps(i1,r1,p1,i2,r2,p2)
DESCRIPTION
This function computes e^i(p1).e^j(p) where r1 is the reference momemtum for e(p1) and r2 is the reference momemtum for e(p2)
INPUTS
* i1 -- an integer, the value of the helicity (= 1,-1) * r1 -- a real array (type ki) of rank 1, shape 4; the refrence momentum * p1 -- a real array (type ki) of rank 1, shape 4; the momentum of the spin 1 * i2 -- an integer, the value of the helicity (= 1,-1) * r2 -- a real array (type ki) of rank 1, shape 4; the refrence momentum * p2 -- a real array (type ki) of rank 1, shape 4; the momentum of the spin 1
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex (type ki)
EXAMPLE
src/module/spinor/eps_prod_sca [ Functions ]
NAME
Function eps_prod_sca
USAGE
complex = eps_prod_sca(i,r1,p1,p2)
DESCRIPTION
This function computes e^i(p1).p2 where r1 is the reference momentum be careful that p2 is assumed to be a lightlike vector
INPUTS
* i -- an integer, the value of the helicity (= 1,-1) * r1 -- a real array (type ki) of rank 1, shape 4; the refrence momentum * p1 -- a real array (type ki) of rank 1, shape 4; the momentum of the spin 1 * p2 -- a real array (type ki) of rank 1, shape 4; a 4-momentum
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex (type ki)
EXAMPLE
src/module/spinor/ket [ Functions ]
NAME
Function ket
USAGE
complex_dim4_1 = ket(p,i)
DESCRIPTION
This function computes the spinor using the chinese's paper Nucl. Phys. B291 (1987) 392-428 equation A.16 modified for non physical configuration E < 0. The functions bra and ket verify the conditions: <-p-|q+> = <p-|-q+> = i <p-|q+> <-p+|q-> = <p+|-q-> = i <p+|q-> <-p-|-q+> = - <p-|q+> <-p+|-q-> = - <p+|q->
INPUTS
* p -- a real array (type ki) of rank 1, shape 4; a 4-momentum * i -- an integer, the value of the helicity (= 1,-1)
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex array (type ki) of rank 2 and shape 4,1
EXAMPLE
src/module/spinor/pslash [ Functions ]
NAME
Function pslash
USAGE
complex_dim4_4 = pslash(p)
DESCRIPTION
This function computes p_{\mu} \gamma^{\mu}, i.e.
p0 gamma0 - p1 gamma1 - p2 gamma2 - p3 gamma3
taking the Chinese convention for the gamma matrices in
Weyl representation
INPUTS
* p -- a real array (type ki) of rank 1, shape 4; a 4-momentum
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a complex array (type ki) of rank 2 and shape 4,4
EXAMPLE
src/module/spinor/scalar [ Functions ]
NAME
Function scalar
USAGE
real = scalar(p1,p2)
DESCRIPTION
This function compute the scalar product of two 4 momentum
INPUTS
* p1 -- a real array (type ki) of rank 1, shape 4; a 4-momentum * p2 -- a real array (type ki) of rank 1, shape 4; a 4-momentum
SIDE EFFECTS
No side effect (pure function)
RETURN VALUE
It returns a real (type ki)
EXAMPLE