m***x
发帖数: 492 | 1 Energy density = ( constatns) T^4 is well know.
But i met a formula with ...=... * sum(n_{l}) over l.
Where l labels the species of effectivelymassless particles,
and n_{l} counts the number of effective degrees of freedom per species:
n_{l} = (number of polarizations) * (number of particles/antiparticles*
1( for boson) /or 7/8 for fermions
Anyone knows this formula and can give me a short explain?
Thanks. | d****y
发帖数: 53 | 2 I guess you should be able find an explanation from
any book on cosmological physics, e.g. Peacock.
Roughly speaking, the distribution function in phase space
is proportional to g_s\eta, where g_s the the spin degeneracy
(number of polarizations), while the difference in the numerical
constant
(1 for boson, 7/8 for fermion) just comes from the fact that \eta is
different for bosons and fermions.
【在 m***x 的大作中提到】
: Energy density = ( constatns) T^4 is well know.
: But i met a formula with ...=... * sum(n_{l}) over l.
: Where l labels the species of effectivelymassless particles,
: and n_{l} counts the number of effective degrees of freedom per species:
: n_{l} = (number of polarizations) * (number of particles/antiparticles*
: 1( for boson) /or 7/8 for fermions
: Anyone knows this formula and can give me a short explain?
: Thanks.
| d****y
发帖数: 53 | 3 Sure. To derive this formula only requires stat. mech. (the $\eta$ I mentioned
is just the mean occupation number for bosons/fermions) One derives the energy
density for each particle sepcies and then adds them up.
I mentioned cosmology b/c the formula you mentioned (energy
density for several particle species) often finds its application in
cosmology: e.g. when you want to consider the energy density of the
universe at a certain epoch, when there're photons, neutrinos, electrons...
【在 m***x 的大作中提到】
: Energy density = ( constatns) T^4 is well know.
: But i met a formula with ...=... * sum(n_{l}) over l.
: Where l labels the species of effectivelymassless particles,
: and n_{l} counts the number of effective degrees of freedom per species:
: n_{l} = (number of polarizations) * (number of particles/antiparticles*
: 1( for boson) /or 7/8 for fermions
: Anyone knows this formula and can give me a short explain?
: Thanks.
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