An O(N) symmetric extension of the Sine-Gordon Equation

Abstract

We discuss an O(N) exension of the Sine-Gordon (S-G)equation which allows us to perform an expansion around the leading order in large-N result using Path-Integral methods. In leading order we show our methods agree with the results of a variational calculation at large-N. We discuss the striking differences for a non-polynomial interaction between the form for the effective potential in the Gaussian approximation that one obtains at large-N when compared to the N=1 case. This is in contrast to the case when the classical potential is a polynomial in the field and no such drastic differences occur. We find for our large-N extension of the Sine-Gordon model that the unbroken ground state is unstable as one increases the coupling constant (as it is for the original S-G equation) and we determine the stability criteria.

arXiv comment21 pages, Latex (Revtex4) v3:minor grammatical changes and additions

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• Classical behavior of deformed sine-Gordon models
• Comparison of renormalization group schemes for sine-Gordon type models
• Many-body parametric resonances in the driven sine-Gordon model
• Large-N approximation for single- and two-component dilute Bose gases
• Phase Structure and Compactness
• A new renormalon in two dimensions
• Coulomb Gas and Sine-Gordon Model in Arbitrary Dimension
• Historical pseudo simplified solution of the Dirac-Coulomb equation
• Renormalisation of non-differentiable potentials