Massive Vertex Operators and Conformal Algebra of the Bosonic Open String Theory in Flat Space-time

TL;DR

This paper develops a systematic method to verify the conformal algebra of massive vertex operators in bosonic open string theory, emphasizing covariant gauge-fixing's role in defining normal-ordering.

Contribution

It introduces a systematic scheme for solving conformal algebra of massive vertex operators, explicitly verifying the algebra at the first massive level in covariant string theory.

Findings

Verified conformal algebra for the first massive level vertex operator

Highlighted the importance of covariant gauge-fixing in normal-ordering

Provided explicit examples of covariant vertex operators

Abstract

A systematic scheme is developed for solving conformal algebra of the massive vertex operators in the old covariant first quantized string theory. Using the first massive level in the covariant spectrum of bosonic open string theory in flat space-time as an example, we explicitly verify the conformal algebra for the normal-ordered covariant vertex operator. We emphasize that the requirement of fully covariant gauge-fixing specifies the form of normal-ordering for massive vertex operators.