Connected Green function approach to ground state symmetry breaking in $Φ^4_{1+1}$-theory

Details Connected Green function approach to ground state symmetry breaking in $Φ^4_{1+1}$-theory Connected Green function approach to ground state symmetry breaking in $Φ^4_{1+1}$-theory

1994-08-23

arxiv.org/abs/hep-ph/9408355v3

Z.Phys. A353 (1996) 301-310

Physics

High Energy Physics

High Energy Physics - Phenomenology

25 Revtex pages, 5 figures available via fpt from the directory ugi-94-11 of ftp@theorie.physik.uni-giessen.de as one postscri

Scientific paper

10.1007/BF01292336

Using the cluster expansions for n-point Green functions we derive a closed set of dynamical equations of motion for connected equal-time Green functions by neglecting all connected functions higher than $4^{th}$ order for the $\lambda \Phi^4$-theory in $1+1$ dimensions. We apply the equations to the investigation of spontaneous ground state symmetry breaking, i.e. to the evaluation of the effective potential at temperature $T=0$. Within our momentum space discretization we obtain a second order phase transition (in agreement with the Simon-Griffith theorem) and a critical coupling of $\lambda_{crit}/4m^2=2.446$ as compared to a first order phase transition and $\lambda_{crit}/4m^2=2.568$ from the Gaussian effective potential approach.

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