[QUE/QFT-06006]

Let \(p^\mu\) be a time like momentum  vector. Let \(n^\mu\)  be a four vector
such that
\begin{equation}
 n^\mu p_\mu=0,  \text{ and } n^\mu n_\mu=-1.
\end{equation}
How many such independent four vectors \(n^\mu\) exist? How that the operators
\begin{equation}
 \Pi^\pm_n =\frac{1}{2}\big(1\pm \gamma_5 \slashed{n}\big)
\end{equation}
are projection operators satisfying.
\begin{equation}
 \Pi^{(+)2}_n = \Pi^{(-)2}_n = I, \qquad \Pi^{(+)}_n \Pi^{(-)}_n =0.
\end{equation}
The notation here is same as in Bjorken and Drell, Gasiorowicz.