M Theory Lesson 194
The denominator of the Fermi function is derived from the partition function
$Z = 1 + \textrm{exp}(- \frac{E - \mu}{kT})$
for the 2 possible occupancies of a fermion state, namely 0 or 1. A ternary analogue resulting in tripled Pauli statistics would require
$Z = 1 + 3 \textrm{exp} (- \frac{E}{kT})$
where we arbitrarily shift the energy scale, momentarily. Presumably this corresponds to the three possible ways of occupying the state with one particle, whereas for ordinary fermions there is only one way of occupying a state. Another interpretation is to write
$3 \textrm{exp} (- \frac{E}{kT}) = \textrm{exp} (- \frac{E}{kT} + \textrm{log} 3)$
where $\textrm{log} 3$ is an energy level (for one prime object) in the Riemann gas system, whose complete partition function is the Riemann zeta function $\zeta (s)$ for $s = (kT)^{-1}$.
$Z = 1 + \textrm{exp}(- \frac{E - \mu}{kT})$
for the 2 possible occupancies of a fermion state, namely 0 or 1. A ternary analogue resulting in tripled Pauli statistics would require
$Z = 1 + 3 \textrm{exp} (- \frac{E}{kT})$
where we arbitrarily shift the energy scale, momentarily. Presumably this corresponds to the three possible ways of occupying the state with one particle, whereas for ordinary fermions there is only one way of occupying a state. Another interpretation is to write
$3 \textrm{exp} (- \frac{E}{kT}) = \textrm{exp} (- \frac{E}{kT} + \textrm{log} 3)$
where $\textrm{log} 3$ is an energy level (for one prime object) in the Riemann gas system, whose complete partition function is the Riemann zeta function $\zeta (s)$ for $s = (kT)^{-1}$.
posted by Kea | 3:13 PM
2 Comments:
This is truly cool. Work is progressing on the paper. I'm writing the section on the mesons. There is nothing like sitting down to write a paper, with the intention that it be understood at a very elementary level, to make one understand something at a deeper level. I hope you do this someday.
Carl, I'm always sitting down to write papers. Oh, I see. You're suggesting I actually finish a few! Hmmm. I'm afraid I have some doubts that anybody will really read them. It took me enough years to figure out that even people with strong opinions about a paper have probably given it no more than a cursory look.
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