Gravitational Properties of Quantum Bosonic Strings

TL;DR

This thesis investigates the quantum gravitational effects of bosonic strings by calculating their energy-momentum tensor, analyzing their gravitational fields, and comparing quantum and classical string properties.

Contribution

It provides the first detailed quantum calculation of the energy-momentum tensor for bosonic strings and explores their gravitational fields in a weak-field approximation.

Findings

The quantum energy-momentum tensor becomes a non-local operator due to quantum fluctuations.

Expectation values are non-zero for both massive and massless string states.

The gravitational field of a quantum string includes multipole moments and radiation.

Abstract

In this thesis we are interested in the study of the gravitational properties of quantum bosonic strings. We start by computing the quantum energy-momentum tensor ${\hat T}^{\mu\nu}(x)$ for strings in Minkowski space-time. We perform the calculation of its expectation value for different physical string states both for open and closed bosonic strings. The states we consider are described by normalizable wave-packets in the centre of mass coordinates. Amongst our results, we find in particular that ${\hat T}^{\mu\nu}(x)$ becomes a non-local operator at the quantum level, its position appears to be smeared out by quantum fluctuations. We find that the expectation value acquires a non-zero value for both massive and massless string states. After computing $<{\hat T}^{\mu\nu}(x)>$ we proceed to calculate the gravitational field due to a quantum massless bosonic string in the framework of a weak-field approximation to Einstein's equations. We obtain a multipole expansion for the weak-field metric $h^{\mu\nu}(x)$ and present its gravitational properties, including the gravitational radiation produced by such a string. Our results are then compared to those found for classical (cosmic) strings.