Covariant Vertex Operators for Cosmic Strings
  We construct complete sets of (open and closed string) covariant coherent
state and mass eigenstate vertex operators in bosonic string theory. By
minimally extending the standard definition of coherent states so as to include
the string theory requirements, we show that the naive construction of the the
closed string coherent states requires the existence of a lightlike
compactification of spacetime. When the null winding states in the underlying
Hilbert space are projected out the resulting vertex operators satisfy the
definition of a coherent state and have a classical interpretation. We present
explicitly both the covariant and lightcone gauge realization of the resulting
states using the DDF map that relates the two. We also identify the
corresponding general lightcone gauge classical solutions around which the
quantum states are fluctuating. We go on to show that both the covariant gauge
coherent vertex operators, the corresponding lightcone gauge coherent states
and the classical solutions all share the same mass and angular momenta and
conjecture that the covariant and lightcone gauge states are different
manifestations of the same state and share identical interactions. This
construction can be used to study the evolution of fundamental cosmic strings
as predicted by string theory and may also be useful for other applications
where massive string vertex operators are of interest.
