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

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.

27 pages, 5 figures, typos corrected

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Cited by in corpus (6)

• Field Theory On The World Sheet: Improvements And Generalizations
• Covariant And Local Field Theory On The World Sheet
• Scalar Field Theories On The World Sheet: A Non-Trivial Ground State
• Scalar Field Theories On The World Sheet: Cutoff Independent Treatment
• More On The Connection Between Planar Field Theory And String Theory
• Field Theory On The World Sheet: Crystal Formation