Consider a collection of freely moving, noncolliding particles that satisfy the collisionless Boltzmann equation 

(a) Show that this equation guarantees that the Newtonian particle conservation law ∂n/∂t + ∇ · S = 0 and momentum conservation law ∂G/∂t + ∇ · T = 0 are satisfied, where n, S, G, and T are expressed in terms of the distribution function N by the Newtonian momentum-space integrals (3.32).

(b) Show that the relativistic Boltzmann equation guarantees the relativistic conservation laws ∇(vector) · S(vector) = 0 and ∇(vector) · T = 0, where the number-flux 4-vector S(vector) and the stress-energy tensor T are expressed in terms of N by the momentum-space integrals (3.33).

Transcribed Image Text:

dN/dl = 0.