CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS410
Origin : M. Hansroul Submitted: 01.09.76
Revision : Revised: 16.12.93
Documentation :
1 Subroutines
Rotations and Lorentz transformation
CALL GLOREN
(BETA,PA,PB*)
GLOREN transforms the momentum and the energy from one Lorentz frame (A) to another (B). It uses the
following input and output:
BETA(4)
PA(4)
PB(4)
(REAL) velocity components in light units of frame B in frame A, BETA(1...3) = ⃗ β, BETA(4)=
(1 − β 2 ) −1/2 = γ;
(REAL) momentum components in the frame (A);
(REAL) momentum components in the frame (B).
GLOREN is called from the routine GDECAY. The momentum ⃗p A and energy E A in reference frame A are
transformed into the momentum ⃗p B and energy E B in reference frame B which translates with velocity ⃗ β
with respect to A:
E B = γ(E A − β ⃗ · ⃗p A )
( )
⃗p B = ⃗p A + γβ
⃗ γβ ⃗ · ⃗pA
γ +1 − E A
CALL GDROT
(P*,COSTH,SINTH,COSPH,SINPH)
GDROT rotates a vector from one reference system to another.
P(3)
COSTH
SINTH
COSPH
SINPH
(REAL) vector to rotate, overwritten on output;
(REAL) cosine of the polar angle;
(REAL) sine of the polar angle;
(REAL) cosine of the azimuthal angle;
(REAL) sine of the azimuthal angle;
GDROT is called from several routines to rotate a particle from in the center-of-mass system to the GEANT
(laboratory) system. The following rotation matrix is used:
⎛
⎜
⎝
cos θ cos φ − sin φ sin θ cos φ
cos θ sin φ cos φ sin θ sin φ
− sin θ 0 cosθ
⎞ ⎛
⎟
⎠ = ⎜
⎝
cos φ − sin φ 0
sin φ cos φ 0
}
0 0
{{
1
}
R φ
⎞ ⎛
⎞
cos θ 0 sinθ
⎟ ⎜
⎠ ⎝ 0 1 0 ⎟
⎠
}
− sin θ 0
{{
cosθ
}
R θ
R θ is a counterclockwise rotation around axis y by an angle θ, and R φ is a counterclockwise rotation around
axis z ′ (rotated by an angle θ from the initial position) by an angle φ.
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