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src/module/spinor [ Modules ]

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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 ]

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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 ]

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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 ]

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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 ]

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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 ]

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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 ]

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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 ]

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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 ]

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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