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- W2080646158 abstract "We apply Kleinert's variational method to field theory and calculate the effective potential of the $ensuremath{lambda}{ensuremath{varphi}}^{4}$ theory in $4ensuremath{-}ensuremath{epsilon}$ dimensions. The potential is regularized in the standard way using dimensional regularization, but we use a nonconventional renormalization scheme to subtract the divergences. This scheme emerges in a natural way when one tries to renormalize the potential before calculating the optimum value of the variational parameter. In order to do this we also have to renormalize the variational parameter. We have demonstrated that this alternative renormalization scheme eliminates the divergences to all orders in the cumulant expansion of the effective potential. We have also tested its compatibility with critical phenomena by calculating critical exponents and the equation of state to order $ensuremath{epsilon}.$ We have shown how to obtain an exact implicit form of the equation of state, which can be solved after performing an $ensuremath{epsilon}$ expansion. The equation of state and the critical exponents coincide to order $ensuremath{epsilon}$ with the usual ones calculated through the loop expansion. The renormalization scheme proposed is also applied to the one-loop effective potential. Even though we obtain the same critical behavior in $4ensuremath{-}ensuremath{epsilon}$ dimensions as in more conventional approaches, our renormalization scheme yields a $ensuremath{beta}$ function that goes to zero in the limit $stackrel{ensuremath{rightarrow}}{ensuremath{epsilon}}0.$ This is an indication that variational techniques and the loop expansion, depending on the renormalization method employed, may be sensitive to the triviality of the $ensuremath{lambda}{ensuremath{varphi}}^{4}$ theory in four dimensions." @default.
- W2080646158 created "2016-06-24" @default.
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- W2080646158 date "2003-09-11" @default.
- W2080646158 modified "2023-09-23" @default.
- W2080646158 title "Alternative renormalization of the effective potential in variational methods and in the loop expansion" @default.
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- W2080646158 doi "https://doi.org/10.1103/physrevd.68.065010" @default.
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