Abstract
Here are collected miscellaneous topics which are helpful in order to understand the former chapters and to make these lecture notes as self-contained as possible.
Like all people who try to exhaust a subject, he exhausted his listeners
Oscar Wilde, The picture of Dorian Gray
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Notes
- 1.
We can choose \(g_i\) slots for the first fermion, \(g_i - 1\) for the second and so on until finally we can choose \(g_i - n_i + 1\) slots for the \(n_i\)th fermion. This gives \(g_i!/(g_i - n_i)!\) and we only used Pauli’s exclusion principle. Until here, then, the order of the chosen particles matter, e.g. having fermion 1 in the first slot is different from having fermion 2 in the first slot. But fermions are indistinguishable, therefore we must divide by \(n_i!\) and hence the result (12.7).
- 2.
Imagine \(n_i\) particles and \(g_i\) slots where to fit them. These slots are separated by \(g_i - 1\) walls. So, compute all the permutations among these objects, which are \((n_i + g_i - 1)!\), but do not consider the permutations among the walls \((g_i - 1)!\) and the particles, \(n_i!\), because they are indistinguishable. So, we find Eq. (12.13).
- 3.
The function \(\Theta (\theta )\) here is not the relative temperature fluctuation and \(\Phi (\phi )\) is not the Bardeen potential.
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Piattella, O. (2018). Appendices. In: Lecture Notes in Cosmology. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-95570-4_12
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