A new approach for nonrelativistic bosonic string in flat space time

A new approach to the study of nonrelativistic bosonic string in flat space time is introduced, basing on a holistic hamiltonian analysis of the minimal action for the string. This leads to a structurally new form of the action which is, however, equivalent to the known results since, under appropriate limits, it interpolates between the minimal action (Nambu Goto type) where the string metric is taken to be that induced by the embedding and the Polyakov type of action where the world sheet metric components are independent fields. The equivalence among different actions is established by a detailed study of symmetries using constraint analysis. Various vexing issues in the existing literature are clarified. The interpolating action mooted here is shown to reveal the geometry of the string and may be useful in analyzing nonrelativistic string coupled with curved background.