Related papers: Two and Three Loops Beta Function of Non Commutati…
We point out that there is a missing portion in the two-loop effective potential of the massless O(N) phi^4 theory obtained by Jackiw in his classic paper, Phys. Rev. D 9, 1686 (1974).
The Fourth order $\phi^4$ model generalizes the classical $\phi^4$ model of quantum field theory, sharing the same kink solution. It is also the dispersive counterpart of the well-known parabolic Cahn-Hilliard equation. Mathematically…
There is strong evidence for the conjecture that the $\lambda \phi^4$ QFT- model on 4-dimensional non-commutative Moyal space can be non-perturbatively constructed. As preparation, in this paper we construct the 2-dimensional case with the…
The previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1…
A nonperturbative method is proposed for the approximative solution of the exact evolution equation which describes the scale dependence of the effective average action. It consists of a combination of exact evolution equations for…
We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $\lambda\phi^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on…
We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $\overline{MS}$-scheme. We do not explicitly compute relevant loop integrals but utilize…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
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…
We obtain analytic results for the four-point amplitude, at one loop, of an interacting scalar field theory in four-dimensional, Euclidean anti-de Sitter space without exerting any conformal field theory knowledge. For the two-point…
We employ the Forcer algorithm to renormalize a variety of six dimensional field theories to four loops. In order to achieve this we construct the Forcer master integrals in six dimensions from their four dimensional counterparts by using…
Renormalization group equations play a central role in effective field theories, both maintaining perturbative control and allowing one to determine the correct low-energy phenomenology. In this work, we complete the one-loop…
In an effort to understand the physical implications of the newly discovered non-trivial directions in scalar field theory, we compute lowest order scattering amplitudes, cross sections, and the 1-loop effective potential. To lowest order,…
We analyze renormalization and the high temperature expansion of the one-loop effective action of the space-time noncommutative \phi^4 theory by using the zeta function regularization in the imaginary time formalism (i.e., on S^1 x R^3).…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
The previously obtained analytical asymptotic expressions for the Gell-Mann - Low function \beta(g) and anomalous dimensions of \phi^4 theory in the limit g\to\infty are based on the parametric representation of the form g = f(t), \beta(g)…
The two loop effective potential of massless $\lambda\phi^4$ theory was presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution was obtained in strong coupling situation in several…
The beta function of the vacuum energy density is analytically computed at the five-loop level in O(N)-symmetric phi^4 theory, using dimensional regularization in conjunction with the MSbar scheme. The result for the case of a cubic…
We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $\lambda\phi^4$ theory in $d=4-\epsilon$, we obtain the full spectrum of…