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Register a new userScheme invariants in phi^4 theory in four dimensions
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We provide an analysis of the structure of renormalisation scheme invariants for the case of $phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes which of course includes MSbar.
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Interacting quantum scalar field theories in $dS_Dtimes M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $lambdaphi_4^4$ theory in the symmetric phase and find the asymptotic behavior $beta(lambda)sim lambda$ of the beta function at strong coupling. Scaling violating contributions to the beta function are also estimated in this regime.
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.
We calculate the next to the leading order Casimir effect for a real scalar field, within $phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.
The next to the leading order Casimir effect for a real scalar field, within $phi^4$ theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Greens function with the Dirichlet boundary condition on both walls. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms, in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. We obtain emph{finite} results for the massive and massless cases, in sharp contrast to some of the other reported results. Secondly, and probably less importantly, we use a supplementary renormalization procedure in addition to the usual regularization and renormalization programs, which makes the usage of any analytic continuation techniques unnecessary.
We compute four-point correlation functions of scalar composite operators in the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N=4 Konishi supermultiplet.
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