Related papers: Constructive Renormalization for $\Phi^{4}_2$ Theo…
The purpose of this work is to rewrite the generating functional of phi^4 theory for the n = 0 and n = 4 correlation functions as the inner product of a state with an observable, as we did in [J. S. Ardenghi, M. Castagnino, Phys. Rev. D,…
A suitable counterterm for a Euclidean space lattice version of \phi^4_n theories, n\ge 4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support…
A scalar field theory with 4-derivative kinetic terms and 4-derivative cubic and quartic couplings is presented as a proxy for quantum quadratic gravity (QQG). The scalar theory is renormalizable and asymptotically free and the remaining…
We construct the $\Phi^4_3$ measure on an arbitrary 3-dimensional compact Riemannian manifold without boundary as an invariant probability measure of a singular stochastic partial differential equation. Proving the nontriviality and the…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the…
In this paper we elaborate on the translation-invariant renormalizable Phi^4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and…
We extend the study of the two-dimensional euclidean $\phi^4$ theory initiated in ref. [1] to the $\mathbb Z_2$ broken phase. In particular, we compute in perturbation theory up to N$^4$LO in the quartic coupling the vacuum energy, the…
For a large class of field theories there exist portions of parameter space for which the loop expansion predicts increased symmetry breaking at high temperature. Even though this behavior would clearly have far reaching implications for…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
The analogue of the loop-loop correlation function in 2d gravity for the planar connected $\phi^3$ diagrams is calculated. It is shown that although the discretized formulas are different the scaling limit is the same as for the loop-loop…
We consider the classical time evolution of a real scalar field in 2 dimensional Minkowski space with a $\lambda \phi^4$ interaction. We compute the spatial and temporal two-point correlation functions and extract the renormalized mass of…
The one-component $\lambda\phi^4$ theory in four dimensions in the spontaneously broken symmetry phase has a non-trivial, non-perturbative sector which can be studied by means of a duality transformation of its Ising limit. Duality maps…
Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are…
In this thesis we investigate aspects of two problems. In the first part of this thesis, we concentrate on renormalization group methods in Hamiltonian framework. We show that the well-known coupled-cluster many-body theory techniques can…
A new technique named Generalized Borel Transform (GBT) is applied to the generating functional of the $\Phi^{4}$ theory in zero dimensions with degenerate minima. The analytical solution of this function, obtained in the non perturbative…
The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally-symmetric massless $\lambda\phi^4$ field theory in the Coleman-Weinberg renormalization scheme $\frac{d^4V}{d\phi^4}|_{\phi = \mu} =…
Interacting quantum scalar field theories in $dS_D\times M_d$ 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…
We study skeleton expansion of $\phi^3$ theory in $6+\epsilon$ dimensions as well as its global symmetry generalizations. We use it to compute the four point function of the scalar field $\phi$ up to $\epsilon^2$. We also do a large spin…
We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency…