Introduction to Vertex Operator Algebras

--- Base version+++ Proposed version@@ -197,7 +197,7 @@ Let  $$-F=\Lambda(\xi_0,\xi_1,\xi_2,\ldots),\qquad \mathbf1=1,+F=\bigwedge(\xi_0,\xi_1,\xi_2,\ldots),\qquad \mathbf1=1, $$  where all generators $\xi_n$ are odd and each state is a finite linear combination of exterior monomials. Define odd operators, for $n\geq0$, by@@ -208,6 +208,8 @@ \psi_{n+\frac12}=\frac{\partial}{\partial\xi_n}. $$ +:::+ The derivative is the left exterior derivative: removing the $i$th factor of a monomial contributes the sign $(-1)^{i-1}$. Thus  $$@@ -221,7 +223,6 @@ $$ \psi(z)=\sum_{r\in\mathbb Z+\frac12}\psi_rz^{-r-\frac12}. $$-:::  The half-integer labels are the usual Neveu–Schwarz mode convention. The field still has integer powers of $z$: in vertex-algebra notation, $\psi_{(n)}=\psi_{n+\frac12}$. Its creation part consists of $r<0$ and its annihilation part of $r>0$.