# Are there negative energies in the bosonic string spectrum?

In the quantization of the open string for example, we are told that the state space is

$$|p \rangle$$

$$\alpha^i_{-1}|p \rangle$$

$$\alpha^i_{-1}\alpha^j_{-1}|p \rangle , \ \ \alpha^i_{-2}|p \rangle$$

and so on...

and, off course, we cannot forget that we have to impose the virasoro constraints:

$$L_n|\psi \rangle=0 \ \ n>0$$ $$(L_0-1)|\psi \rangle=0$$

There are some problems with the tachyon but I would like to ask that in a separate question, so let's see the next state $\alpha^i_{-1}|p \rangle$. I know that $p^2=0$ must hold for this state, but is there any restriction for the value of $p_0$? Are there $p_0<0$ states in the spectrum? Are they banning the negative-energy solutions by hand?

• To my knowledge there is no such restrictions for p0 separately. I think this is like the other question：is there any restriction for point particle quantum state to have nagetive p0，isn't it？ – Kangle Aug 8 '17 at 21:27
• Yes, I am doing a parallel between both theories. But there are people saying (confusing me) that there are no negative $p_0$ in the point particle, that the point particle doesn't have any issue. See this question – MoYavar Aug 8 '17 at 21:59