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

Abstract

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.

25 Revtex pages, 5 figures available via fpt from the directory ugi-94-11 of [email protected] as one postscript file (there was a bug in our calculations, all numerical results and figures have changed significantly), ugi-94-11

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• Pion Properties in a Hot $\Pi N\Delta$ Gas
• Microscopic analysis of two-body correlations in light nuclei
• Two-Body Correlations in Pionic Systems

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