U102 Lorentz Transformations

LORENF transforms the momentum 4-vector of a particle from the Lorentz-frame $\Sigma$ to the frame $\Sigma \text{'}$ like LOREN4 (U101); it is faster than LOREN4 because the rest-mass M of $\Sigma \text{'}$

is passed as an argument to save the square root.

LORENB executes the inverse transformation.

Structure:

SUBROUTINE subprograms
User Entry Names: LORENF, LORENB

Usage:

CALL LORENF(SM,SP,PB,PF)	forward transformation	PB -> PF
CALL LORENB(SM,SP,PF,PB)	backward transformation	PF -> PB

with

SM

Rest-mass M of system $\Sigma \text{'}$ with $M2=E2-P2$ .

SP

Momentum 4-vector $(P,E)$ of $\Sigma \text{'}$ in $\Sigma$ .

PB

Momentum 4-vector $(p,e)$ in $\Sigma$ .

PF

Momentum 4-vector $(p\text{'},e\text{'})$ in $\Sigma \text{'}$ .

Method:

For LORENF (cf. LOREN4 (U101)):

$e\text{'}$	$=$	$(eE\; -\; pP)/M$
$p\text{'}$	$=$	$p\; -\; P\; (e+e\text{'})/(E+M)$

because $pP=eE-e\text{'}M$ and $pP-e(E+M)=-M(e+e\text{'})$ .

For LORENB:

$e$	$=$	$(e\text{'}E\; +\; p\text{'}P)/M$
$p$	$=$	$p\text{'}\; +\; P\; (e+e\text{'})/(E+M)$

$•$

U111