Quantum Action Principle for Covariant Systems. Bosonic string

TL;DR

This paper introduces a novel covariant quantum theory for free bosonic strings using a quantum action principle, where stationarity conditions are applied at the quantum level to define physical states with fixed energies.

Contribution

It proposes a new covariant quantum framework based on a quantum action principle, differing from traditional approaches by imposing stationarity conditions at the quantum level.

Findings

Defines physical states as stationary states obeying the quantum action principle

Ensures stationary states have well-defined energies

Provides a covariant quantum description of free bosonic strings

Abstract

A new form of covariant quantum theory based on a quantum version of the action principle is considered for the case of a free bosonic string. The central idea of the new approach is to delay conditions of stationarity of the classical action with respect to Lagrangian multipliers up to the quantum level where delayed conditions of stationarity are imposed on a quantum action. Physical states of the ordinary covariant quantum theory are replaced by well defined stationary states as those which obey quantum action principle. The stationary states have well defined energies.