In Barton Zwiebach's *A First Course in String Theory*, in section 14.4, there's a fermion counting operator $(-1)^F$ which is supposed to give you $+1$ if the state is bosonic, or $-1$ if the state is fermionic. For a general state $\lambda$ he says

The eigenvalue of $(-1)^F$ on a state is equal to minus one times a sequence of factors of minus one, one for each fermionic oscillator that appears in the state.

This is probably a very trivial question, but is this extra minus one simply because the Neveu Schwarz ground state (the Neveu Schwarz vacuum) is *chosen* to be fermionic (and all states are constructed by applying appropriate creation operators on this fermionic vacuum)? Why is it conventionally chosen to be fermionic? At least the way Zwiebach has written, it looks like a choice.

This post imported from StackExchange Physics at 2015-03-10 12:56 (UTC), posted by SE-user leastaction