Currently I'm trying to understand string theory in the light cone quantization. I just have had a look into Polchinski (Vol. 1, Introduction to the bosonic string), because – as far as I could see – GSW doesn't cover Vertex Operators in the light cone formulation (correction appreciated).

There he constructs (almost) general states on page 21 (eq. 1.3.28) via raising operators acting on Fock space vacuum states $\left|0;k \right\rangle$ with $k = (k^+, k^i)$. A few sentences later he introduces the state $\left| 0;0 \right\rangle$ for the ”ground state of a single string with zero momentum“. I think this state does not even exist as $$p^- = \frac{p^i p^i + m^2}{2 p^+}$$ diverges. This can equivalently be concluded by the fact that $\left|0;k \right\rangle$ (with arbitrary $k$) is a tachyonic state which can never have zero momentum.

This is problematic as this state is heavily used e.g. in chapter 2.8 (eq. 2.8.2 ff.).

Is there anything wrong about my arguments?

This post imported from StackExchange Physics at 2015-03-01 12:39 (UTC), posted by SE-user Florian Oppermann