Unconstrained Variables of Non-Commutative Open Strings

TL;DR

This paper derives unconstrained canonical coordinates for bosonic strings in a non-zero B-field background, facilitating a more natural framework for quantization by handling boundary conditions as second class constraints.

Contribution

It introduces a method to project canonical coordinates onto the constraint surface, resulting in unconstrained variables for string quantization in non-zero B-field backgrounds.

Findings

Derived unconstrained string coordinates from second class constraints.

Provided a framework for quantization using these unconstrained variables.

Simplified the treatment of boundary conditions in string theory.

Abstract

The boundary conditions of the bosonic string theory in non-zero $B$-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the constraint surface we derive a set of coordinates of string that are unconstrained.These coordinates represent a natural framework for the quantization of the theory.