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The vacuum structure of N = 2 linear supersymmetry (LSUSY) invariant QED,which is equivalent to N = 2 nonlinear supersymmetry (NLSUSY) model, is studiedexplicitly in two dimensional space-time (d = 2). Two different isometriesSO(1,3) and SO(3,1) appear for the vacuum field configuration corresponding tothe various parameter regions. Two different field configurations of SO(3,1)isometry describe the two different physical vacua, i.e. one breaksspontaneously both U(1) and SUSY and the other breaks spontaneously SUSY alone.

On vacuum structures of N = 2 LSUSY QED equivalent to N = 2 NLSUSY model