Related papers: $\phi^3$ theory at six loops
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We…
We study the $\phi_{\star}^4$ model for a scalar field in a linearization of the Snyder model, using the methods of the Worldline Formalism. Our main result is a master equation for the 1-loop n-point function. From this we derive the…
The idea of reduction of couplings in renormalizable theories will be presented and then will be applied in Particle Physics models. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group…
We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar…
Explicit two-loop calculations in noncommutative $\phi^4_4$ theory are presented. It is shown that the model is two-loop renormalizable.
Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the ${O}(n)$-symmetric $\phi^4$-theory in $D=4-\ep$ dimensions we present the…
We provide an origin of family replications in the standard model of particle physics by constructing renormalizable, asymptotically free, four dimensional local gauge theories that dynamically generate the fifth and sixth dimensions with…
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
The prescription for the $\gamma_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
The sunset diagram of $\lambda\phi^4$ theory is evaluated numerically in cutoff scheme and a nonzero finite term (in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This finding…
We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $\phi^Q$. Within the OPE framework, the anomalous dimension of the $\phi^Q$ operator is…
Leading-twist operators have a remarkable property that their divergence vanishes in a free theory. Recently it was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leading-twist…
We investigate Non-Hermitian quantum field theoretic model with $\iota g\phi^3$ interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field $\phi$. We analytically calculate the 2-loop $\beta$ function and analyse…
We introduce tropical scalar field theory as a model for renormalizable quantum field theory, and examine in detail the case of quartic self-interaction and internal $O(N)$ symmetry. This model arises in a formally zero-dimensional limit of…
Massless $\phi^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $\phi ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We present three-loop formulas for the additive renormalization constant A(u,epsilon) and associated renormalization group function B(u) for the specific heat of the O(n) symmetric phi^4 model. Using this result, we obtain also the…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…