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Dynamical symmetry breaking of $λϕ^4$ in two loop effective potential

The two loop effective potential of massless $λϕ^4$ theory was presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution was obtained in strong coupling situation in several prescriptions except the Coleman-Weinberg prescription. The beta function in the broken phase becomes negative and the UV fixed point turns out to be a strong coupling one, and its numeric value varies with renormalization prescriptions, a detail in difference from the asymptotic free solution in one loop case. The symmetry breaking phase was shown to be an entirely strong coupling phase. The reason of the relevance of the renormalization prescriptions was shown to be due to the non-perturbative nature of the effective potential. We also reanalyzed the two loop effective potential by adopting a differential equation approach basing on the understanding that takes all the QFT's as the ill-defined formulations of the 'low energy' effective theories of a complete underlying theory. Then the relevance of the prescriptions of fixing the local ambiguities to physical properties like symmetry breaking was further emphasized. We also tentatively proposed a rescaling insensitivity argument for fixing the quadratic ambiguities. Some detailed properties of the strongly coupled broken phase and related issues were discussed.