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  1. Is a Universe with only a single fermion anomalous instead of free from anomalies?

(e.g. electron, defined through fermi statistics with exchange statistics with a gained $-1$ sign, or rotating 360 degree to get $-1$ sign on the wavefunction.)

  1. More generally, is a Universe with only an odd number of fermions anomalous instead of free from anomalies?

Note: In Solid State systems, it seems that the ground state always have an even number of fermions. The global symmetry properties of the system usually depend on the number of fermion $(-1)^F$, the fermion parity $\pm 1$ sign. For the whole system, we usually have $$(-1)^F=(-1)^{even}=1.$$

Is there a no-go theorem for any reason? such as (global) anomalies? What may be the constraints on the emergent gauge fields for the fermionic system?

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  • $\begingroup$ This is too broad. Please specify what you mean by "The Universe with a single fermion". $\endgroup$
    – Prof. Legolasov
    Commented Jan 7, 2017 at 4:57
  • $\begingroup$ I believe they're thinking about a hypothetical universe that contained only one fermion. But I have no idea how to answer the question itself. $\endgroup$
    – Michael Seifert
    Commented Jan 11, 2017 at 17:50

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