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 4thorder for theλΦ 4-theory in 1 + 1 dimensions. We apply the equations to the investigation of spontaneous symmetry breaking, i.e. to the evaluation of the effective potential at temperatureT=0. Within our momentum space discretization we obtain a second order phase transition (in agreement with the Simon-Griffith theorem) and a critical coupling ofλ crit /4m 2=2.446 as compared to a first order phase transition andλ crit /4m 2=2.568 from the Gaussian effective potential approach.
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Communicated by: A. Schäfer
Supported by DFG, BMFT, KFA Jülich and GSI Darmstadt part of the dissertation of A. Peter
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Häuser, J.M., Cassing, W., Peter, A. et al. Connected Green function approach to symmetry breaking inΦ 41+1 -theory. Z. Physik A - Hadrons and Nuclei 353, 301–310 (1995). https://doi.org/10.1007/BF01292336
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DOI: https://doi.org/10.1007/BF01292336