String in noncommutative background: another approach
  We propose a model action in 1+1 flat space-time (compact in spatial dimension) embedded in D flat space-time with a non dynamical space-time dependent two vector. For the above constrained system Dirac brackets of suitably defined co-ordinates turn out to be non zero and under specific choice of the two vector the model action reduces to a general action of open string in a noncommutative background where we find the natural embedding of the open string action of in presence of magnetic field on D-brane. 
R.Bhattacharyya