This paper explores the possibility of covariant string quantization in Minkowski space of four dimensions using a method the author calls “bosonization”. The work is motivated by the absence of experimental evidence for the additional space-time dimensions proposed by other string theorists.
The author regards as promising an approach which replaces standard Hamiltonian structures for the original classical models with alternative Hamiltonian structures. If there are to be no anomalies in the Poincaré algebra formed by the corresponding quantized dynamical invariants of the string, and if the dimension of space-time is assumed to be 4, then there are restrictions on the choice of the Hamiltonian variables. These variables must be chosen so that, on subsequent quantization, relativistic invariance is maintained.
This paper describes part of the author’s program to establish a self- consistent string theory in four dimensions.