Mean Field Method Applied To The New World Sheet Field Theory: String Formation

TL;DR

This paper applies the mean field method to a world sheet field theory for phi^3, confirming previous variational results and enabling the calculation of excited states that resemble a string spectrum with linear trajectories.

Contribution

It introduces the mean field approach to the world sheet theory, providing a new way to analyze both ground and excited states, and clarifies the string formation mechanism.

Findings

Mean field results agree with variational calculations.

Excited states form a string spectrum with linear trajectories.

String spectrum can be separated from the continuum by parameter tuning.

Abstract

The present article is based on a previous one, where a second quantized field theory on the world sheet for summing the planar graphs of phi^3 theory was developed. In this earlier work, the ground state of the model was determined using a variational approximation. Here, starting with the same world sheet theory, we instead use the mean field method to compute the ground state, and find results in agreement with the variational calculation. Apart from serving as a check on the variational calculation, the mean field method enables us to go beyond the ground state to compute the excited states of the model. The spectrum of these states is that of a string with linear trajectories, plus a continuum that starts at higher energy. We show that, by appropriately tuning the parameters of the model, the string spectrum can be cleanly seperated from the continuum.