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U101 Lorentz Transformation

Routine ID: U101
Author(s): TCLibrary: KERNLIB
Submitter: J. ZollSubmitted: 01.03.1968
Language: FortranRevised: 27.11.1984

This routine transforms momentum and energy of a particle from one Lorentz-frame to another.

Seen from the reference system Σ , the other system Σ' has the velocity β , with η= γβ .

If a rest mass M is tied to system Σ' , with energy E and momentum P , we have:

β= P/E, η= P/M, γ= E/M.

The momentum and energy of a particle with mass m is
in system Σ p and e = p2+m2 ,
in system Σ' p' and e' = p'2+m2 .

Structure:

SUBROUTINE subprogram
User Entry Names: LOREN4

Usage:

    CALL LOREN4(S,A,X)
with the 4--vectors S= (P,E) and A= (p,e)

calculates the transformed 4--vector X= (p',e') .
LOREN4 contains one square-root to derive M from P and E.

Method:

If we split p= pL+ pT

into components parallel and normal to β , where

pL= {pηη2} η, pT= p-pL,

we can write the transformations as

p'L= γ pL-η e, p'T= pT, e' = γ e - ηp

and get
p' = p+ (γ-1)pL- e η

= p+ η ((γ-1)pη2- e)

= p+ η (pη/(γ+1) - e)&sp;(because ofη2= γ2-1)

= p+ P (pP/(E+M) -e)/M,

e' = γe - ηp

= ( eE-pP)/M.

U102



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Next: U102 Lorentz Transformations Up: CERNLIB Previous: T604 Solution of


Janne Saarela
Mon Apr 3 15:06:23 METDST 1995