Non Trivial Saddle Points and Band Structure of Bound States of the Two Dimensional O(N) Vector Model

Details Non Trivial Saddle Points and Band Structure of Bound States of the Two Dimensional O(N) Vector Model Non Trivial Saddle Points and Band Structure of Bound States of the Two Dimensional O(N) Vector Model

1994-04-22

arxiv.org/abs/hep-th/9404143v1

Nucl.Phys. B433 (1995) 625-656

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, latex twice, epsf figs in separate uuencoded file, UTTG-03-94

Scientific paper

10.1016/0550-3213(94)00505-9

We discuss O(N) invariant scalar field theories in 0+1 and 1+1 space-time dimensions. Combining ordinary ``Large N" saddle point techniques and simple properties of the diagonal resolvent of one dimensional Schr\"odinger operators we find {\it exact} non-trivial (space dependent) solutions to the saddle point equations of these models in addition to the saddle point describing the ground state of the theory. We interpret these novel saddle points as collective O(N) singlet excitations of the field theory, each embracing a host of finer quantum states arranged in O(N) multiplets, in an analogous manner to the band structure of molecular spectra. We comment on the relation of our results to the classical work of Dashen, Hasslacher and Neveu and to a previous analysis of bound states in the O(N) model by Abbott.}

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