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

J. M. Haeuser; W. Cassing; A. Peter; M. H. Thoma

doi:10.1007/bf01292336

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arXiv · hep-ph/9408355

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

J. M. Haeuser·W. Cassing·A. Peter·M. H. Thoma

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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 $λΦ^4$-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 $λ_{crit}/4m^2=2.446$ as compared to a first order phase transition and $λ_{crit}/4m^2=2.568$ from the Gaussian effective potential approach.

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J. M. Haeuser, W. Cassing, A. Peter, M. H. Thoma. 1994-09-12. Connected Green function approach to ground state symmetry breaking in $Φ^4_{1+1}$-theory. https://doi.org/10.1007/bf01292336

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