Related papers: Soft symmetry improvement of two particle irreduci…
[Abridged] n-Particle Irreducible Effective Actions ($n$PIEA) are a powerful tool for extracting non-perturbative and non-equilibrium physics from quantum field theories. Unfortunately, practical truncations of $n$PIEA can unphysically…
The effective potential of the Standard Model (SM), from three loop order and higher, suffers from infra-red (IR) divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal…
Resummations of infinite sets of higher-order perturbative contributions are often needed both in thermal field theory and at zero temperature. For instance, the behaviour of the Standard Model (SM) effective potential extrapolated to very…
We propose a novel method of evaluating the effective action, wherein the physical one- and two-point functions are obtained in the limit of non-vanishing external sources. We illustrate the self-consistency of this method by recovering the…
We investigate the linear response of an O(N) scalar quantum field theory subject to external perturbations using the symmetry improved two particle irreducible effective action formalism [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594…
The Symmetry Improved Two-Particle-Irreducible (SI2PI) formalism is a powerful tool to calculate the effective potential beyond perturbation theory, whereby infinite sets of selective loop-graph topologies can be resummed in a systematic…
Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and…
Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…
Symmetry is a cornerstone of quantum mechanics and materials theory, underpinning the classification of electronic states and the emergence of complex phenomena such as magnetism and superconductivity. While symmetry breaking in density…
The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its…
We consider the two-loop Phi-derivable approximation for the O(2)-symmetric scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's theorem in…
The Shallow Ice Approximation (SIA) model on strong form is commonly used for inferring the flow dynamics of grounded ice sheets. The solution to the SIA model is a closed-form expression for the velocity field. When that velocity field is…
Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local…
The free space Maxwell dielectric problem can be reduced to a system of surface integral equations (SIE). A numerical formulation for the Maxwell dielectric problem using an SIE system presents two key advantages: first, the radiation…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their…
Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the…
In this paper, we propose a generalized successive approximation method (SAM), called invariantly admissible policy iteration (PI), for finding the solution to a class of input-affine nonlinear optimal control problems by iterations. Unlike…
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop…
Semilocal density-functional approximations (DFAs), including the state-of-the-art SCAN functional, are plagued by the self-interaction error (SIE). While this error is explicitly defined only for one-electron systems, it has inspired the…