Editing String field theory (section)

===Gauge invariance ===
These properties of the cubic vertex are sufficient to show that <math> S(\Psi) </math> is invariant under
the [[Yang–Mills]]-like gauge transformation,
:: <math> \Psi \to \Psi + Q_B \Lambda + \Psi * \Lambda - \Lambda * \Psi \ , </math>
where <math> \Lambda </math> is an infinitesimal gauge parameter.  Finite gauge transformations take the form
:: <math> \Psi \to e^{-\Lambda} (\Psi + Q_B )e^{\Lambda} </math>
where the exponential is defined by,
:: <math> e^{\Lambda} = 1 + \Lambda + \tfrac{1}{2} \Lambda* \Lambda + \tfrac{1}{3!} \Lambda * \Lambda * \Lambda + \ldots </math>