Four momentum
Create and test for four-momentum
## S3 method for class '4mom' Ops(e1, e2) ## S3 method for class '4mom' sum(..., na.rm=FALSE) vel_to_4mom(U,m=1) p_to_4mom(p,E=1) as.4mom(x) is.4mom(x) fourmom_mult(P,n) fourmom_add(e1,e2)
x,P,e1,e2 |
Four-momentum |
p |
Three-momentum |
E |
Scalar; energy |
U |
Object coerced to four-velocity |
m |
Scalar; rest mass |
n |
Multiplying factor |
...,na.rm |
Arguments sent to |
Four-momentum is a relativistic generalization of three-momentum, with the object's energy as the first element. It can be defined as mU, where m is the rest mass and U the four-velocity. Equivalently, one can define four-momentum as (E/c,px,py,pz) where E is the energy and (px,py,pz) the three-momentum.
Function vel_to_4mom() converts three-velocity to four-momentum,
and function p_to_4mom()) converts a three-momentum to a
four-momentum.
The function Ops.4mom() passes unary and binary arithmetic
operators “+”, “-” and “*” to
the appropriate specialist function.
The package is designed so that natural R idiom may be used for physically meaningful operations such as combining momenta of different objects, using the conservation of four-momentum.
For the four-momentum of a photon, use as.photon().
Robin K. S. Hankin
# Define 5 random three velocities: v <- r3vel(5) # convert to four-velocity: as.4vel(v) # Now convert 'v' to four-momentum, specifying rest mass: vel_to_4mom(v) # 4mom of five objects with 3vel v, all unit mass vel_to_4mom(v, 1:5) # 4mom of five objects with 3vel v, masses 1-5 vel_to_4mom(v[1],1:5) # 4mom of five objects with same 3vel, masses 1..5 # Now convert 'v' to four-momentum, specifying energy E: p_to_4mom(v,E=1) p_to_4mom(v,E=10) # slower p_to_4mom(v,E=100) # even slower # Four-momentum of objects moving closely parallel to the x-axis: P <- vel_to_4mom(as.3vel(c(0.8,0,0)) + r3vel(7,0.01)) reflect(P) reflect(P,c(1,1,1)) sum(P)
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