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.

O(N) symmetric extension of the sine-Gordon equation / Cooper, F; Sodano, P; Trombettoni, A; Chodos, A. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - 68:4(2003), pp. 1-10. [10.1103/PhysRevD.68.045011]

O(N) symmetric extension of the sine-Gordon equation

Trombettoni, A;
2003-01-01

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.
2003
68
4
1
10
045011
https://arxiv.org/abs/hep-th/0304112
Cooper, F; Sodano, P; Trombettoni, A; Chodos, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32976
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